I believe the story of Ais being 1000 years old is misleading. I think she has memories of that time, or implanted memories from someone else.
It is more likely that the current Ais was born FROM the dungeon itself for a purpose, maybe similar in the way the Xenos came to exist. However, in her case, since she has spirit blood, it is likely the dungeon was waiting for the right time to spawn her...as part spirit.
To be a little more clear, I think the Xenos themselves are part human, part monster, given lingering souls from those killed in the dungeon (a fusion of human and monster souls).
Since Ais was found in the dungeon, alone, it is possible she was spawned at a certain time, and possibly even in front of at least one of the loki familia captains...and it has yet to be revealed to others, including Ais herself, of how she was ACTUALLY found (a top secret that only certain persons are aware of).
The truth may be that Ais either died long ago in the dungeon, or she was created from someone else that died long ago, at the age of 7, or she may have been absorbed by the dungeon. the honest truth is no one truly knows everything about how the dungeon works, not even the gods, and since she was found in the dungeon as a 7 year old girl, with no one having seen her before wandering around at a younger age, the best guess would be the dungeon itself being the answer to her only being 7 yet having memories from long ago.
so far, there has been no evidence that time traveling/portals would exist in the story or be possible. cryostasis/cryonics is not that likely either as someone would have noticed her sooner.
I am sure in the near future it will be time to reveal her origiins and method of preservation in the main story (Bell has just started to see a possible connection between her father's last name and Ais last name at the end of LN 15). I also have a feeling that Hestia will eventually have to tell Loki about Bell's secret, reveal how he feels about Ais, and the fact Ais has helped him train to become better. I have a feeling it will be after Loki finds out from another god who Bell's grandfather is, and it is likely that as a result of learning those secrets Loki will share who Ais parents really are...and maybe a hidden item in her status that no one knows about.