Trying to pivot out of AM and into HF, doing MSc Finance at LSE to help but what else

So as the title says, I’m trying to pivot out of Asset Management and move to a HF.

Experience: - research analyst at mid tier AM, generalist coverage - investment consulting as a grad job - spring week at IB - BSc in Maths and Actuarial Science from top 30 uni

I essentially want to move because 1) the AM I work at is really slow moving, the other analysts have no drive/hunger and are pretty comfortable to just trudge along. I’m still early in my career, and this environment imo is holding me back. The pay is also extremely below market (as told by recruiters).

So I’ve scoured for some advice on here on how to break into HF, it seems they tend to mostly hire from IB. I’m going to be doing a Masters in Finance at LSE (part time), in hopes this will help boost my CV. But essentially, I’m looking for advice on what next steps to take? Summer Internship > FT for couple yrs > HF? Or do I have luck with my CV going straight to HF?

Also quite interested in private debt, currently in fixed income so private debt is something I’m quite open to.