Transitioning from data science in the tech industry to quantitative finance?

I've been working as a quant/data scientist in the tech industry for some time, and now I'm thinking about moving to quant/trading work in finance. What is the best way for me to do this? If I were looking for a new job in the tech industry, I know many people here and could find an inside connection to many companies, but the problem is that I don't know many people who work in finance, and I'm wary of blindly uploading my resume to a website. Is there a better way?

About me, if it matters - I work at a top tech company (think Google, Facebook, Palantir, etc), I've worked full-time or interned at several other top tech companies in the past, and I went to a top school (think Harvard, Stanford, MIT, etc; it's strange that I don't know anyone who works in finance given this, but all my friends either went into tech or grad school). I do a lot of statistics, machine learning, and software at my job. I'm well known and well respected in my field (I've had offers from almost all the top tech companies at some point), but I can't help but feel like I need an "in" to finance.