Could the universe create itself with a time loop?

This is precisely what is envisioned in Gott and Li’s self-generating universe hypothesis.

Their proposal is based on the assumption that the spacetime defined by general relativity can be curved and connected in non-trivial ways, in addition to the fact that closed time-like curves (CTC) are also allowed.

One of the possible mechanisms would be the following: a metastable vacuum space subject to inflation expands, producing an infinite number of other vacuum bubbles, which occasionally become, via quantum tunneling, a new expanding vacuum, a child universe.

Because of the possibility of closed time-like curves, it is mathematically possible for the new generated universe to be the same as the space that generates it.

Thus, it seems that the laws of physics allow the universe to be its own parent and to generate itself in a time loop.