In addition to what everyone else has said, run the codebase through a LLM, and ask it questions. If the code is private and privacy is a concern, look into self-hosting the LLM. You might not be able to analyze the full repo yet, but you can inspect modules separately, and get a mental model of the codebase quicker than if you were manually inspecting it.

Also, read any technical documentation about the product, team/company processes, etc. You can quickly get an idea of how well the product is maintained if the documentation is up to date. If not, then submitting documentation patches is a good first step your teammates will appreciate.