How to enter a fintech startup?

First off, which country are you based in? 

I understand that Start-ups in general are usually not accessible to new graduates because they don't have the resources to train and develop talent, they prefer folks work 1-3 years in consulting (management consulting, IT Enterprise or otherwise), finance (IB/VC scope), accounting (Audit within F.S. or TMT) or Prod Management or FInOps within a mid-sized financial technology firm with direct transferrable skills developed there. Obviously, the scale and scope of work you do in your previous work will determine which roles you qualify for in the Startup. 

For instance, if you worked in management consulting, that most closely correlates with strategy & ops positions within FinTech startups. If you did IB/VC, you may be in a more Corp Dev or internal M&A team and if you did accounting, it would be Corp. Fin or Financial Analyst type work. You could also try for product management if you worked on technical consulting projects with the digital teams. 

If you're hoping to join out of school, then you may need to network, show and prove interest/competence at these firms and see what their hiring timeline is like. With SVB going under, starts ups are strapped for cash, coupled with the latest economic pressures of the recession. With that said, I just read a thread about consulting firms deferring new hire start dates, so I can't imagine these firms are in a strong position to hire in the near-term.