Question on the singularity theorem
It does not have to start from the big bang. There are also different universe models such as the big bounce. Where the universe has an infinite past, such that it expands and then contract.
See
https://www.quantamagazine.org/big-bounce-models-reignite-big-bang-debate-20180131/
https://www.wired.com/story/what-if-the-big-bang-was-actually-a-big-bounce/
For more detailed explanations you can look some cosmology textbooks