I believe the inverse, I think most kids out of school should start at a (good) large company, they have the resources and framework to provide all kinds of career training you'd never get from startups or small companies. Mentors, leadership training, technical skills training, much bigger budgets, and a smaller group of tasks that someone is expected to perform. The pace is likely more deliberate, if not even boring, and that is good. As a newcomer you'll get a front row seat into what processes really work (code reviews, source control [yes, I still run into old/new people who don't use/believe in it], documentation, etc.) and you will be able to see how not having them can be detrimental in the future.
Starting off in a startup will lead to little support and a cowboy attitude, what the world needs more of is people who know when to cowboy, and cowboy with purpose rather than using 'just get shit done' as an excuse for a lack of standards and quality.
Also, this has been MY career experience to this date. As I now run my own tech companies and have been hiring technical people for the last 7 years, I have anecdotally found this to hold true. The early to mid-career types that have only ever been at tiny companies or startups are really good at having a breadth of experience and an ability to move fast. The spent all my career with big company types have usually been pretty deep at something (a language, framework, tech niche) and are very used to processes. They're typically slower and have a need to encumber small things with bloat (process, tech, etc). Marrying these people together on a team has yielded me fantastic results in nearly every case. The big enterprise people feel like they've been released from a cage, and the scrappy startup types seem a little less feral, while providing an infectious get shit done attitude.
Starting off in a startup will lead to little support and a cowboy attitude, what the world needs more of is people who know when to cowboy, and cowboy with purpose rather than using 'just get shit done' as an excuse for a lack of standards and quality.