Best route to enter Europe (including UK) IB/PE from India?

Hi everyone,

Some background info on me : 

I am a final year undergrad from a target engineering university in India (IITs, BITS Pilani), majoring in Computer Science with a minor in Financial Economics. Expect to graduate with a GPA of around 8/10 (slightly above 8).  My grades in all my Finance courses are pretty strong: 9.5/10. I have an S&T internship at an Asian IB and have an internship lined up at a BB (think, MS/GS/JPM) in their IBD (MO role) before graduation. Aiming for a score around 730-760 in the GMATs (I gave the 1st GMAT official practice test to check my base level without any prep and scored a 650). Also planning to complete CFA L1 before graduation. I have also been learning French and German over the summer.

I wanted advice on the best ways to move into IB/PE in Europe via a Master's program. I aim to apply for the Master's programs starting in 2024 at HEC Paris, LBS MFA, Oxford MFE, and HSG MBF. My main criteria for selecting a program is the ease of securing an IB/PE FT opportunity post-graduation (in Europe/UK).

Considering my profile and everything else, I had the following queries:

1) Is my profile good enough to recruit for IB/PE SA roles straight away? If not, how can I improve it?

2) Which program will best position me to recruit for IB/PE roles in Europe/UK (not as decided on location right now, but I would love to work in continental Europe considering I should be at least at a B2 level in German/French when I join for Masters)?

3) Should I prefer a 2-year Masters(HEC MiM) over a 1-year Masters(HEC MiF, LBS MFA, etc.) considering the 6 months off-cycle internship opportunities in Europe?

4) How accepting is HEC or HSG for non-EU students like me? Will recruiting there be possible(in France or Switzerland)?

Any advice/opinion will be greatly appreciated.