My approach is to learn the stack (read books, sketch/prototype).

Get the team to whiteboard the architecture with you. This is better than existing documentation because you will get the full commentary and start building a mental model of the software.

Ask the team about problem areas.

Don't push on major stack/architecture changes until you know the stack/architecture.

Make sure the base engineering practices are there. You should have a seamless workflow from pre-merge code reviews, testing, and deploy.