What automated tests do, though, is make it significantly easier to test. You will find bugs faster, and dramatically shorten the amount of manual testing that you need to do.
IMO, the best way to learn TDD is via experience. You need to work with a team that's willing to support a junior engineer. From a senior engineer's perspective, the amount of handholding that some junior developers need through writing decent unit tests is quite time consuming.
Thus, if I were you, I'd just be selective about who I work for. I'd look for a team that's willing to be patient while I learn, and that has enough senior developers that I can learn by following a good example. A team that wants a lot of experience in this or that is probably not able to allow you the time needed to learn.