Profile evaluation for MFE 2023

Hi everyone!

Could you please help me evaluate my profile for MFE 2023? I am wondering if it's competitive enough for the programs in the US and Europe. Unfortunately, my only exposure to finance was through my work experience and I am anxious that the lack of fundamental financial knowledge might hurt my applications.

For 2022-2023 academic year I was admitted into an Applied Math program at a mid-tier university in Europe. However, I doubt that this degree will help me with landing a quant job with a top trading shop or HF. Seems like the brand recognition of the university is pretty important.

Here is my profile:

1) BSc in Applied Maths and CS from a top institution in my country. Graduated in 2022 with honors, GPA 9/10, top 5% of the department.
2) My curriculum was heavy on ML and its theory; hence, a lot of probability theory, statistics, linear algebra, and optimization. I am also confident in my coding skills (C++, Python, a bunch of other languages).
3) I have around 2 years of TA experience (discrete math, algorithms and data structures, ML) and 2 years of RA experience at ML-focused labs (mostly natural language processing).
4) I have one first-author publication at a workshop in a top ML conference. Another publication is currently in review.
5) Did 2 SWE internships --- one at a large software company and one at an international investment bank.
6) Currently I have 5 months of full-time work experience as a quant researcher in a small investment fund. I plan to continue working as a quant during my gap year.
7) As for recommendations, I am going to ask my thesis advisor and a professor, with whom I wrote my research papers.

I am currently looking into FE programs at top French universities (El Karoui and such) as well as ETH Zürich and EPFL. Can you give me suggestions on how to improve my chances?
What is missing from your profile now that prevents you from getting a Quant/FinEng role? Otherwise is it the case that you need an MFE degree to be considered at the top trading shops and HFunds that you've targeted?