Did I go off the Beaten Path too Early? Need Advice

I'm currently a senior at a target school. Was never one to care much about brand name and cared a lot more about gaining as much experience as I can. Have done internships at very reputable boutiques (not EBs) and will be headed to a reputable boutique as well for fulltime (think Dyal, Foros, Broadhaven). Ended up choosing the firm bc of how great the team is and the traction the firm is getting but ended up turning down a BB and EB offer in the process. I do want to pursue PE in 2-3 years at an UMM ideally doing either buyout or growth equity (ok with MM or megafund as well). Given that my firm doesn't have the prestige and brand name as a GS or Moelis and so much of recruiting is driven by headhunters, I am wondering if I have effectively shot myself in the foot by going off on my own so early?

For those wondering why I turned down the better-known firms, the firm I joined has much greater upside and exposure to the senior guys who are all top-notch with some opportunities to do principal investing work, which I felt to be more valuable. I also got final rounds for PE analyst programs at several firms at the megafund and UMM level so I had hoped that I would be still competitive come associate recruiting...