What year does Starbound take place?

I think it could take place a few hundred years from now, given these conditions. Warning though, my reasoning dangerously assumes Starbound is realistic to the way earth (and the solar system) is.

Starbound has humans take on an american military theme
17k years a supervolcano is due to end civilization (unless they could fix that)
50-100k years a glacial period could occur (unless they could fix that too)
Mars was being terraformed in starbound
The time when pluto was considered a planet is still remembered by most
Saturn is shown (and said) to still have its rings, which will be gone in 300m years
Uranus is shown to still have it’s ring, and the absurd seasonal tilt, which will be gone in 1 million years
Venus was planned to be terraformed before the Earth incident

A codex in game reads:
"A United Earth
Many centuries ago the Earth was governed in a seemingly endless tide of shifting hierarchies; empires rose and fell, nations grew to prominence and collapsed, and wary peace was established only to implode. This volatility spanned millennia.

The Earth we know today was forged when Humankind turned to the stars. At this time resources, once scarce, became abundant, and a shift took place: we recognised both our insignificance and our significance within the universe.

Instead of expanding our settlements across the stars, we began to look inward, to strive for balance and a sustainable way of life with the support of newly acquired resources, and to build a solid future for our beloved Earth"
And to that I say; nothing is ever really lost to us as long as we remember it.

It says "Many centuries ago..." and "This volatillity spanned millenia.", using both hundred and thousand measurements. Although I don't believe you can say, "A hundred years ago from today, it was terrible, but 1000 years after a 100 years ago, things changed." because then you're talking about 900 years in the future. So when it says Many centuries, it probably means, many many many. Since millenia is plural, it would have to be at least 2000 years, which is over 20 centuries of course. I think it's safe to assume "shifting hierarchies; empires rose and fell, nations grew to prominence and collapsed" to be a reference to things such as the roman empire, and all the wars that happened afterward up to the world wars.
BUT, since it says "This volatility spanned millennia.", and the volatillity started when civilization was refined enough to form groups and ways to access each other to wage wars. 2000 years from the start of the roman empire (for example) would be 1973. But, obviously, "millenia" rarely means rounded to the nearest thousand. 1000 years is really really long in terms of everything, that's a lot to skip. In this case it probably has a definition closer to "This many thousand years but i dunno how many hundred.". Which is great, because we're still stuck with it probably being from 2100 AD to 3000 AD.
BUT BUT, with Mars' colonization still not completed at the start of starbound, and the fact that they haven't even touched Venus. I think, given humanity's eagerness to spread to other worlds, that cuts it down by a lot. Mars could take 500-1000 years to terraform, but that number varies wildly. Thus, my final guess is 2300-2800 AD. About as specific I think is possible

 

Hmm, some interesting ideas here, here are my thoughts based on research in game and in Wargroove, which according to CF themselves (and the presence of the Floran/Nuru and all the references Nuru makes to SB in game) takes place in the same universe as SB:

I believe someone here has already noted this, but one codex (A History of Space Travel) mentions "several thousand years of peace and prosperity" following the discovery of FTL, giving us our largest estimate for how far in the future SB takes place.

According to the wargroove wiki (unfortunately I couldn't find the specific source from the game directly) "Thousands of years ago, the continent was split between two rival kingdoms: Cacophony in the west, and Silmor in the east." This quote referring to the continent of Aurania where the game takes place.

With these in mind, having both ends use thousands of years in a vague sense means that things can conveniently be made to line up quite easily. However, given that a lot changes in even a single thousand years and humanity had ftl travel at least two millennium but don't come off as hyperadvanced and dominating a good chunk of the galaxy as one would expect in that timescale, I'm going to choose the lowest available option and say that humanity has had ftl for 2000 years. Now that's still a timescale where one would expect humanity to be as I mentioned, but I have a solution to that issue: an utterly devastating war that for once, truly ended all full scale wars among Humanity, call it the "Final War" if you will. I say this because humanity is largely pacifistic in vanilla SB and that the notion of Humans having stl space travel is considered laughable at this point, which I feel implies some lost history. After all this war happens before the development of FTL, so the 2000 years of peace afterwards still stand. The Final War could have been nuclear, chemical, biological, or even a long and population grinding conventional war, most likely a combination of them that would leave Humanity's population a shadow of its former self and Earth on the brink of collapse. Whatever population that survived would be all in on spot, ideally Earth's moon. The reason why I choose Earth's moon is that it'd easily be spared by the war on Earth, and leave such a population in the most convenient spot to discover Erchius and thus FTL. Earth managing to barely cling to life however would still have small smatterings of survivors of it's own, so while left horrified by the war they had witnessed, rather than peace out and leave the solar system for a new planet to call home, this lunar population would return to their homeworld to help rebuild the human population and restore Earth. Although one group from the moon, eager to try out FTL technology, would end up trying to establish a colony somewhere out in the galaxy, only to loose contact with the rest of Humanity and be assumed dead, further reinforcing humanity's focus on restoration rather than expansion at this point. This rash attempt would end up far off course and crash lands on an alien planet, where it's left unsalvageable to the surviving humans. These survivors end up having to start from scratch and establish the human kingdoms we see in Wargroove. Meanwhile the restoration of Earth and Humanity would take about 1500 years, especially as regrowing the population would take some time, in addition to decontaminating entire regions of the planet. It would only be at the end of this stage that Humanity would start to look outwards. Despite being around for the entirety of this time, FTL would only be used within the Sol system to expediate the extraction of resources, Humanity in fact being spurned to start exploring the galaxy when said resources started to become scarce again and FTL finally began to be used fully.

I mention resource scarcity being the initial driving factor of Humanity looking outward as that's what A United Earth establishes, rather than establishing mining outposts or colonies, humanity would come into contact with the Hylotl (and then the other races soon after), their initial interaction with aliens being a positive one, they eagerly form an economic partnership with the Hylotl, gaining a stream of resources, and becoming the biggest customers (and source of employees) of Letheia. The encountering of alien civilizations also helps give rise to the Terrene Protectorate, as Humanity's Redemption implies. It's worth noting that the Terrene Protectorate isn't the Human Government here, but more likely a part of it at best, especially considering the Terrene Peacekeepers. The way it's presented in game comes across more like an exploratory humanitarian organization, not to mention one that's only 500 years old, making it much too young to work in the timescale I've settled on here. It's also worth noting that humanity is not represented by the Protectorate logo, but their own flag (even in the intro mission itself).

All in all, this puts SB a bit more than 2000 years into our future, maybe with a decade or even a century attached.

However, there is one final wrinkle to deal with, and that's when we revisit Wargroove's lore, specifically regarding Higher Vampires. There are two confirmed Higher vampires in Wargroove's lore (with there being likely more), Sigird, who's 987 years old, and her unnamed predecessor, about 4000 years old. Furthermore lore directly from the game states that "High Vampires are not born, but created. When a High Vampire decides the time is ripe, they wait until the dead of night, and then steal into a nearby village to kidnap the most readily available human infant. The process of changing that infant from human to High Vampire takes 13 months, and is done using a kind of magic innate and exclusive to the vampiric races." The fact that the passage mentions humans specifically does seem to thrown a wrench into my timeline here, and having the years simply go by faster on Aurania due to it being a different planet only creates a new issue with the ages of the commanders in the game, although I suppose an argument could be made that they're adjusted to Earth years and could be older in Auranian years. I think it's possible that previous higher vampires weren't human, and that Sigrid is in fact the first Human higher vampire to exist on Aurania, her master being some other more native species such as a harpy, merfolk, or most fitting, a deepfolk. I suppose either of these solutions suffices, although I suppose it's also not impossible that humanity was blasted back to the stone age and took far longer to rebuild, but I find that stresses my admittedly pretty flexible suspension of disbelief too much, so I prefer my previous two ideas on how to reconcile things here. I suppose we could also pull a star trek here and have the humans be the result of some aliens abducting an entire human population sometime before present day, or maybe there's some time dilation going on with Aurania, but those options just feel too bizarre to me.

Despite the wrinkle presented at the end there, piecing together Humanity's history in SB like this is part of why I love the game and it's lore, and I'm honestly not too bothered by the wrinkle wargroove adds in anyways.

TLDR: Probably about 2000 years into our future.

edit: thinking about it "the Final War" might be a tad bit too dark to fit into SB narratively, sure SB is chock full of things that are honestly quite dark when you think about them, but the lack of mention for a singular pivotal event also makes me think that instead of some great war that truly ended all wars, Human civilization as we know it reached the brink of collapse thanks to constant warring and wanton environmental destruction. The moon thing could still work fine though.