Way too late to the game, should I just wait for an MBA?

Background:

• Senior at a target school interested in Public Finance 
• Middle office Internship during the summer, currently have a return offer
• Econ and liberal arts coursework

Problem: Got onto the IB train too late

I came into college wanting to be a lawyer, and only became interested in finance after my internship this summer. Specifically want to go into Munis because of my policy background, but I'm pretty sure I'm fucked already with trying to get something out of undergrad. Been trying to coffee chat people so far but hasn't yielded any good results in terms of connections to full-time or even just beefing up my resume with better work experience. I know the market is crap especially for college students and ESPECIALLY for seniors about to graduate but the effort has been demoralizing. 

Am I fooling myself? This entire existential crisis has been stressing me for the past 4 months and I feel like I'm deluding myself into thinking I can break in this late. At this point my plan is to get the GMAT out of the way so I can pivot into the industry through an MBA after a few years of working in middle office. Any advice from people more experienced than me would actually be really appreciated.