I would start with a basic question: what do you want to do? Your current job let you explore a lot of topics and roles: which did you like best? Which do you see yourself pursuing for the next few years? Your post seems to imply that you’re looking for management roles but it’s unclear as whether it’s because that’s what you like to do or because that’s what you feel you should do to grow your career. Word of advice: it’s much easier to have a successful, fulfilling career doing what you love than eating shit every day doing something you don’t like (management, architecture, product, whatever) but that you think is good for your career.

Once you’ve figured out what you want to specialize in (and make no mistake, in a larger company you’ll have a narrower role than in a startup), write your resume around those skills. Market yourself (write a blog, try to speak at conferences, etc) as an expert in that topic. Identify what shortcomings you still have and work on them through side projects, reading books, taking an online course, etc. When you get to the interview stage and people point out your lack of expertise, explain (better yet, demonstrate through relevant examples) that working at a startup has taught you to pick up new skills quickly. Convince your future manager that it’s in her benefit to recruit someone who knows how to learn new skills rather than a one-trick poney, even if the poney is very good at its one trick.