Worth applying for S&T/Prop? - BSc -Pure Maths

2.8 GPA cumulative (i know, its absolute trash) I'll put this being so low down to me absolutely hating the &*$^ out of the university experience.

3.9 GPA for Mathematics major

no experience apart from bookkeeping for family business no extra curricular of note, other than developing a statistical system to profit from spread betting. Unsure of whether what is considered "gambling" is something that can be counted as an extra curricular activity. I also trade AUD/EUR and CL intraday.

Is it worth applying to prop firms ie Optiver, Liquid Capital etc and/or S&T divisions at banks and other financial institutions?

Or is it a foregone conclusion and there is no point?

If that's the case, what are my options if I am set on becoming an institutional trader?

ie start in back office, or start at a small firm, take a bullet in the brain because there is no point etc.

Thanks.