Of note to the "has the life support been on all this time" questioners, it's worth noting that the opening credits are of the Destiny coming to life, lights coming on bit by by and what looks like air flowing, etc. Then the gate starts spinning, activates, and people come flying through. Implying, anyway, that activation (perhaps the first failed one) signaled to the ship to turn on life support.
You may be right. I not necessarily arguing against your observation. There were parts of the show I didn't see, either time. But six minutes, and I think that was what was mentioned, is not a lot of time to oxygenate, much less warm a large craft. Especially not with a malfunctioning environmental control system, where it would have to work that much harder to create a suitable environment. I don't even recall seeing steamy breaths from a chilled atmosphere. But if the leak were bad enough then heat would evaporate rapidly through the gases. Of course I don't know exactly what you mean by the first failed attempt (I think I do but if I'm not mistaken why would a failed attempt trigger an activation routine, I assume contact was not really established).
Of course I don't know the limits of the environmental technology involved, just what was encountered after they boarded, don't know of the opening scenes you described was followed sequentially and immediately by the humans boarding (it could have implied something else - but then again I didn't see the details), or what exactly the writers were or weren't thinking about. Also we don't know of the ship geared up the entire ship's environmental immediately, or just the small "receiving area" we've seen so far. It would be a lot easier to environmentally prepare a small area for occupation rather than the whole ship and that may accost for the closed off sections, and the half-way open doorway. But I'm still betting on former boarding.
It would far better explain the door, and let's say the ship sat idle for a long time (had reached it's final detonation or embarkation point, from the ancient point of view), or was still hopping around from time to time, what are the odds, given the premise of the show that alien life is relatively abundant throughout the universe, even star-going alien life, that no-one else would have discovered that ship over a very long stretch of time, and every potential discoverer had just ignored it? (I personally would have investigated immediately upon discovery.) Course it could be designed to disguise, or conceal itself. Other ancient technology does. In a case alike that it would be, can the ship be caught if it runs or if it is sitting still how good are alien sensing devices versus how good is the on board camouflage or concealment? (assuming it ahs any.) It would be submarine warfare.
But if I get to see it tonight, maybe the onboard crew will start making internal ship discoveries while the exploratory team is operating off-board. They certainly have enough personnel to explore on-board assuming they can do so without too quickly burning up their atmosphere on board. A lot of people working will burn up their oxygen rapidly, and if they penetrate to other areas no guarantee yet those areas are inhabitable.
Still, they should see if they can rig something that will temporarily allow them to transfer some of the habitable environments of the places they do visit, back through the gate, and into the ship. But I don't see they have the equipment or technology available among their own gear. If they found out they could take manual control of the vessel and maneuver it and stop the FTL clock, or at least pause it a few days, then I'd take the whole ship and land it on a planet with a good atmosphere, and environmentally flood it that way. It's a disease risk, for sure, but it beats slow asphyxiating.
Well, I got one more thread to reply to and then back to work. I enjoyed reading what I could of the speculations this morning. Some clever ideas and observations.