Sign up for AngelList (http://angel.co) and set up a career profile that emphasizes your data skillset and startup experience. You should be an interesting candidate for Product Management and Growth positions, so start by contacting those.
AngelList makes it easy to quickly contact many companies, but I highly recommend you pick just a handful of highly interesting prospects and reach out with a note explaining why you'd be a great fit.
network for intros, preferably warm.
failing that, just email the CEO directly. write a kickass email pitching yourself and detailing your skills. tactfully follow-up.
network some more.
founders have (and want to see) passion and hustle. show them you have these qualities and you shouldn't have trouble landing a paid internship if not an entry-level role.
last resort: get a few unpaid internships at startups you love. if one doesn't turn into a full time offer, you'll have some awesome experience you can use to get the attention of other startups.
AngelList makes it easy to quickly contact many companies, but I highly recommend you pick just a handful of highly interesting prospects and reach out with a note explaining why you'd be a great fit.