How to Break into Trading from Statistics Background

Hi all,

I am (formerly) a PhD student in statistics who just dropped out this summer after completing my MS. I am now looking for a role, and I am considering trading as a possible career path. I will not be targeting the hypercompetitive HFT firms, except maybe a YOLO application to some less selective firms like SIG etc. 

It seems to me that breaking into S&T is a very regimented process (have to land an internship and then convert to full-time). Additionally, my graduate program is reputable but definitely a non-target.

I have a few questions:

(1) What is the best approach to getting my foot into the door? Is heavy networking required / what seniority level of traders should I be contacting?

(2) How should I be preparing for interviews? I believe my math and coding skill is sufficient but I have no finance knowledge besides Black-Scholes on a very theoretical level. 

(3) What is the overall vibe and outlook of entering an S&T career, compared to entering tech?

I would greatly appreciate any advice that you guys have. Thanks!