[allthesethings]

You don't necessarily have to convince the manager, given a few prerequisites: it's possible to get at the code and build it locally, and you're willing to go around the team and do testing on your local machine. Not an easy task, unsupported, but it can be chipped away at over time, and if the project really is as stuck as it's made out to be, there will be parts of it that aren't changing rapidly and make for good low-hanging fruit.

Gradually that test suite will accumulate enough stuff that all OP has to do is walk into work, pull the latest, and make a few easy fixes before they finish coffee. They will look like either a hero or a monster, depending on how the politics work out. It's risky, but either way something will have been stirred up.