Patent boutique lateral to big law?

I’m currently a 2L going to my states top law school (ranked around 70). I got an EE degree (3.8 gpa) and I’m currently ranked right around the median. If upon graduation I take a job at a local boutique patent firm (assuming I do prosecution), what’s the likelihood I can successfully lateral to a big law or close to big law pay mid law patent prosecution position a few years down the line? If I got a shot, how would I go about doing it? What’s the competition like for those positions?