Product Management Break

Hi, I am looking to break into Product Management. Not sure where to start and what works on the street. I have a view that experience always trumps pedigree and certifications, but to start with at least I need an opportunity to prove my worth. It would be great if the experienced folks who hire in the field or someone who has transitioned to PM can delineate how to crack into a PM role.

For me, PM Roles fall in 2 categories: 1) PM tech & 2) PM Business growth

Education: - BS-MS (Dual Degree) Mathematics - IISER Pune - PGPBA IIM Bangalore Experience: ~ 4 years, mainly working in Data Science, AI & Analytics

Also, if you can discuss what can be an expected pay for the role. (Current Base 35 LPA)