Yes, you can. You have to submit safety information, but you're not barred from entering the market. From an article about a supplement that was essentially an unregulated drug because it was an
unknown drug:
> Under a 1994 federal law, supplement makers must submit some kind of safety data to the F.D.A. if they plan to introduce new ingredients to the market. And manufacturing-practice rules require them to make sure their products contain only the ingredients listed on the labels, with no hidden substances. But, unlike drug makers, supplement makers are not required to prove that their products are safe and effective on humans. Nor do they have to get federal approval before selling their products. That means it is up to the F.D.A. to identify any risky supplements from among the estimated 85,000 on the market, and to prove that they are adulterated or present health hazards.
https://www.nytimes.com/2013/03/17/business/a-soldiers-paren...
Again, the onus is on the FDA to find supplements that are previously unknown, regulated drugs. If we flipped the requirements, supplement makers would be barred from selling their supplements without clearing them with the FDA first. The active drug in that story has since been banned by the FDA: https://www.fda.gov/food/dietarysupplements/productsingredie...
You're not allowed to make specific medical claims. But you are also not required to show any efficacy for what you do claim, and the supplement industry regularly gets as close as they can to "specific medial claim." And sometimes they cross it! And, again, the onus is on the FDA to find such cases.