Sophomore Internships for Quant Trading?

Currently a rising sophomore mathematics major. I would like to preface that I am very aware that breaking into quant trading from undergrad is an absurdly difficult feat, but I am still curious.

The most common sophomore internships I have seen seem to be either research, SWE at FAANG or a Startup, Data Science type roles, or lower level quant funds. My question is: how bad is deviation from this path?

If I did an internship in non-quantitative finance (PE/VC/AM etc.) over my sophomore summer, would this totally kill any chances I had at a junior-year internship in quantitative trading? How much (if at all) could quantitative projects/coding projects fill this gap?

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