Cosmetic products that do not contain color additives, or other materials that require approval for use, do not require FDA approval prior to marketing.
In contrast, cosmetic products that belong to the over-the-counter (OTC) category require listing of the drug product(s) and drug substance(s)/active ingredient(s) that are added to the cosmetic products. Cosmetic manufacturers and packaging companies (outside the US) who want to export their products to the US are committed to registering their foreign establishments, factories and manufacturing facilities.
To the article “Regulations and Registration for Cosmetics, Cosmetics and OTC Products”