Whether it's common or not, is this the right place for you? Stepping into a tire fire for your first job runs the risk of burning you out early and cementing lots of bad habits.

If you do want to stay there, there's a vast happy medium between "no tests at all" and "test driven development". Check out the "git effort" command for a list of the most-changed files in the codebase. (If it's not installed, try looking for a "git-extras" package for your operating system.)

The files changed most frequently are often also the ones most in need of refactoring and tests. If nothing else, you can cobble together a little test suite of your own and be the guy that finds bugs faster and introduces fewer new bugs.