Early Career Transition to Hedge Fund

Would appreciate any and all advice on the below process I plan on taking to transition to working at a hedge fund.

Graduated in '25 from a B+ tier university with an engineering honors BS and physics BA. Working in project finance, but would ultimately like to become a quant researcher (beginning to understand that title can be ambiguous). Resume pretty much matches most requirements having machine learning projects in R/Python, taking classes like quantum mechanics, having industry experience, and wrote a "top of the class" level thesis. 

I am looking to begin submitting applications for summer '26 positions (after finishing one year at my current role). I believe it would be most effective to submit applications early (nowish) and understand the feedback so that I may have an opportunity to apply to graduate schools before that deadline closes. 

Would also appreciate commentary on attractive advanced degrees for quant researchers (and from what schools). 

Thanks for the help!