Last time I was in the same boat, I tried to identify the major components of the project and then fixed small bugs and/or implemented a small feature in each of them. You get basic exposure to everything and you can explore from there.

I’ve also asked to be notified of every code review for the project. It’s hit and miss, but you get some exposure to different parts of the project, what’s done where, and how they interact when your colleagues add functionality / fix bugs.

And use the project like a customer to get an idea of how it works and what you can do with it, what problem is solves, what works well and what doesn’t.