Is this Oxygen (2021)...?
A woman wakes in a cryogenic chamber with no recollection of how she got there. As she's running out of oxygen, she must rebuild her memory to find a way out of her nightmare.
A woman wakes up in a cryogenic pod with approximately ninety minutes worth of oxygen remaining. She doesn't know who she is, why she's in the pod, or where it is (she can't see outside), but initially assumes it's somewhere on Earth.
The pod contains an AI named M.I.L.O. (Medical Interface Liaison Officer) which is monitoring her vital signs. She can converse with it and it grants her access to a database containing news articles, images and videos, but it won't open the pod without an authorisation code, and when she asks it what her name is, it identifies her simply as Omicron 267. After asking M.I.L.O. to run a DNA scan on her, it informs her that her DNA matches that of Elizabeth Hansen, a doctor specialising in cryogenics. Viewing images of Hansen and her husband triggers some fragmented memories and more surface as the film progresses, but, for now, most of her life remains a blank to her.
It subsequently transpires that she's not on Earth after all, but on an automated colony ship transporting ten thousand people in pods like hers to a planet in another star system. The other passengers are asleep, as she's meant to be; she awoke due to a malfunction caused by an asteroid collision. The ship's purpose is to ensure the continued existence of the human race, since a deadly virus has broken out on Earth and is expected to kill everyone there within two generations.
After viewing a video of a presentation on memory-transference technology given by an elderly Elizabeth Hansen, Omicron 267 also realises she's a clone of Hansen, implanted with her memories. The other passengers on the ship are clones with implanted memories as well, created in a sterile environment and kept insulated in order to prevent them from contracting the virus and carrying it to the other planet.
This is a French-language film, but you didn't say which language you watched it in and you may have seen a dubbed version. If it is the right film, then M.I.L.O.'s periodic updates on how much oxygen Omicron 267 has remaining would equate to the time limit you mentioned.