appropriate time to start applying for internships/jobs

i’m a fresh grad doing a one year master’s program at business school this coming fall and am trying to break into finance (prev. in the performing arts industry).
yes, there is career networking at my school, but i’m literally competing with everyone else in my program so i want to branch out. however, most internships are only open to undergrads or mba students (and i’m neither) with very specific graduation timeframes.
would i have more luck applying to full time jobs later, after im almost done with my master’s or should i just shoot my shot and apply to internships anyway? thank you!
about me: BA in econ, cs & music minors, previous internships in music entertainment and academia, living in chicago