Transition from Pub Fin IB to S&T

Hey everyone, 

This is my first post on WSO. I am super grateful for all of the career alpha. Here is my situation:

I am an incoming public finance analyst at a top BB muni shop (BofA/JP/MS/etc). I went to a mega target university for undergrad (UofPenn/Harvard/MIT/etc) and did my summer analyst stint at the same BB.

I really thought that I wanted to do Pub Fin because I loved politics and learning about how cities function. However, in my senior year, I worked at a small quant/crypto hedge fund (3-10B AUM) and I realized that my true interest lies in markets and S&T.

Is it possible for me to make the transition to a trading FICC desk at my BB? How should I go about making the transition? Do I have to grind out my two years as an analyst first before asking to move internally? Or should I just attempt to recruit for FT at a different bank?

Would appreciate any guidance, thank you.