That was not necessarily a mistake. As a fresh college grad (and particularly as an engineer) I'd argue that you are ill-equipped to judge a good startup opportunity from a bad one. There is absolutely nothing wrong with spending time at a large company, benefitting from their experience in graduate intake, learning a lot of good, sensible practises, then applying them to a startup.

I've also recently become deeply skeptical of working for a startup as anything other than a founder or a very early employee. You don't benefit monetarily (low pay, bad stock options) and the work environment is frequently toxic and incredibly demanding. The only difference is you'll be making your bosses rich instead of making stockholders rich.