In my field at least it’s a better path to start at the bigs and move to a smaller shop after you’ve built up a base level of professionalism, competency, work ethic, and work habit. Large companies tend to have very well designed development programs and career paths that are geared to provide incremental learning with each new experience and generally the things that they teach you early in your career will serve you well no matter where you end up.
Small company experience can be great but it is very dependent on personalities (many of whom work at small companies because they couldn’t cut it in a larger or more formal environment). In my experience, I’ve found that the people who find success at small companies are the ones with the competency to know what good looks like and the confidence/certainty to become one of the personalities that actually shapes the environment. These are characteristics that many 20-somethings just don’t yet have.