Do you have any chance of producing academic work good enough to get at least into a workshop at a major machine learning conference like ICLM, ICLR, or NIPS? Or into something machine-learning adjacent such as ACM FAccT (conference on fairness, accountability, transparency etc in ML)? Employers are actively looking to hire people at these conferences and having a good poster can make you stand out. Statistics overlaps a lot with ML and workshops offer lots of niche areas where you may try to become the big fish in the small pond.

Hackathon is great. Don't worry about going in with an idea, especially if it's your first my suggestion is to join an existing team and help with whatever you can. Great way to network and learn if you take that approach. 

 there's often an intro session at the start, meant to link people up into teams. If you find a hackathon you like, and don't see this on the schedule, reach out to the organizers ahead of time, or even on the first day, they likely have a list of teams looking for people. Worst case, they'll link you up with other individuals and you can start a team from scratch. You can also check the community reddit/discord/etc ahead of time. The organizers have an incentive to get this right, even for socially awkward (not saying you are) participants.

 how do I find and join an existing team?

Maybe check out 80k's career advice (if you haven't already): 

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Our career guide covers everything you need to know about how to find a fulfilling career that does good, from why you shouldn’t “follow your passion,” to why medicine and charity work aren’t always the best ways to help others. It’s full of practical tips and exercises, and at the end, you’ll have a draft of your new career plan. 

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