Clerking without relationships with law school professors

I’m a junior litigator and have become increasingly interested in a clerkship. I dropped the ball in law school, largely because I simply did not know how the application process worked/how early I would have had to start applying.

I was a very average student at a good law school, so was told by career services I’d struggle to find a clerkship without taking a few years to work. I am now seriously thinking about applying, but did not develop any close relationships with professors in law school such that I feel I am unfortunately screwed.

For people who managed to secure federal clerkships who were in my (or another analogous) position, how did you do it? Any advice would be appreciated.