As a hiring manager, residual concerns that I would try to get a handle of in interview would be:
* How do you deal with solving problems in larger systems, particularly in code you did not design, write, or perhaps even knew existed up to the point of discovering a problem
* Typical team work and communication problems.
If you have no other experience you can point to, I'd take one or two of last year's AoC puzzles you solved and write a short write-up on how you solved it. Explain the problem, explain why it's hard (it's a challenge after all), talk about failed attempts (this is important), and talk about how you solved it.
I'd include this with your resume or cover letter.
Remember, the goal is to get to the next stage of the interview process - so you want to give them something to signal you're worth interviewing. AoC (or open source work) gives the interviewer something to ask about.