Tackle the backlog - those bugs that have been just sitting there for months or even years because other things keep getting prioritized above them. They may be minor, low-priority fixes, but when you solve them, what people will think is "Wow! This developer fixed a bug that no one else could in 3 years! That's always annoyed me but now it's finally fixed!". Next thing you know, they'll be giving you the most important tasks.

Along the way, you'll of course need to talk to people to understand both the code that has the bugs and what is expected of it, and you'll learn years of history from both the development side and the product side, which is invaluable.