Founder of Sunray Ops, People Ops lead for 10+ start-ups. Employee first mentality
First: define what 'startup' tier you're most interested in. Post-seeding, Series A, Series B, Series C, etc, etc. They all have unique quirks and have varying headcount needs depending on their recent investments.
Second: determine what product you'd like to focus on. SaaS, BaaS, FinTech, MarTech, etc. This will help determine the kind of customer and issues you'll likely encounter.
Third: review recent startup news via investment firms (Incubators, Accelerators and VC's) or tech articles (techcrunch, builtin, crunchbase). These will list recent funding news or companies on the cusp of rapid growth. Remember: funding = double or tripling headcount, often in Product or Technology.
Forth: determine if your skills or interests can translate to Tech or Data roles. Being a versatile candidate will appeal to any hiring manager. If you have time, taking a few side courses will only emphasize your candidacy further.
Fifth: apply directly to the site, even (especially) without a job posting listed. This works best with Series A or seeding companies as the inboxes are often still being manually reviewed. Even more so, startups often don't know they need a role until it's an immediate start. Get in early to make a lasting impression.
Sixth: reach out to employees at the company. Ideally those in Product teams but any Individual Contributor can work. (Avoid Sr Managers/Founders as they are always being messaged; IC's enjoy offering referrals).
Seventh: If/When in an interview, 8 times out of 10, the format will be more casual. Mirror the interviewers style and be friendly and driven. Give answers based on When/Why/How/What to showcase knowledge. Don't ask about benefits, longevity, remoteness or company success: they're often just getting started and will mostly be remote.
Notes: most true startups won't be on the main job boards (Indeed, Linkedin, WeWorkRemotely) as they haven't yet established the People Ops infrastructure required to filter those pools of candidates. Y Contributor and Pallet are decent options, based on their prior investor links but finding the startup's websites themselves is the best solution.
TL:DR - Look for non-direct avenues (recent articles, team member profiles, investment firm listings) to improve your chances. The startups will appreciate the tenacity (I sure do when I run recruiting for Startups). Good Luck!