Jumping from Mid-market M&A advisory to Bulge bracket

Hi, I currently work for EY within their Tax team and I have been trying really hard to transition into M&A. After 9 months of rigorous search, I got an offer at a boutique corporate advisory team specializing in M&A. I wanted to work for a bulge bracket bank but it seems way too competitive with my limited experience in M&A. I just wanted to know would it be hard for me to jump to bulge bracket bank later on, lets say after 2 years of working for a mid-market bank? I just need some advice. Thanks guys!