Difficult but not impossible OP.
The hard part - getting an interview. Referral is your best bet, and most well known firms have a strict filter on undergraduate colleges ("tier 1" college only) at screening level. You may have better odds of luck at relatively lesser known firms.
The part you have control on - work really well on interview prep, leave nothing to chance. A lot of case work, guesstimate, framework application & answers crafted for your background, reason to switch and mid/short term aspirations. Usually hiring panels are 3 to 4 rounds, and you'll need to be judged as a bar raiser in at least one + above expectations in 2 to make a clean cut. Good luck!