Speaking broadly about not only Jane street, but adjacent firms like Jump and Citadel: In my experience (working with and getting coached by a recruiter in the space), these finance companies really want you to love the space, not just the technology. I wasn't able to drink the kool-aid or fake enough die-hard passion for trading to get far in the their interview process, despite having extremely relevant technical capabilities
Some are also very elitist with respect to your pedigree, so even amazing experience but no degree from a top US school can make it difficult (yes, even a decade later..)
Apply, like anywhere else. Most quant firms expect you to be pretty strong with C++, but since they use OCaml (and don't expect you to know that) I think you can get away with low-level systems experience more broadly.
No direct experience but I would imagine you would need solid intermediate skills at OCaml, probably being a nerd enough to make your own extensions or the ecosystem for benchmarking and debugging, not just coding. Then a liberal dose of projects about OCaml, game theory, and financial markets. That ought to get their attention at least.
What I've heard is that they target graduates from elite schools, bonus points if you did maths or CS competitively. Everything else, including OCaml and finance, they claim that they can teach you. Although they always go to functional programing conferences like ICFP to promote their company, so they must hire language experts as well.
I applied there 15 years ago. They asked me some logic puzzles and some typical quant interview probability questions. It wasn't about OCaml at all even though I do have an OCaml background and I thought I interviewed for a SWE position. I remember the interviewer was unpleasant for no reason.
A friend of mine interviewed there recently, he got some typical leetcode questions (hard ones).
There has always been a mystery around it since back in my college days.