There are regulatory and in-market control differences between regions and countries worldwide. A product may be fully compliant in the US, while at the same time additional testing/information may be needed for the EU and labels and claims may need to be adjusted. And the EU requires that an EU based legal entity or person assumes responsibility for the products as the "Responsible Person".
The EU Cosmetics Regulation regulates many key aspects, for example: production has to be in line with GMP principles; the raw materials that you source have to be well documented (e.g. MSDS, TDS, CoA); your formulations have to be compliant with the substance bans, restrictions and quality requirements; the claims that can be made for cosmetic products are regulated and enforced and may require substantiation; and it is important to understand the duties and responsibilities you and/or your importers into the EU have.
Knowing the basics early on, even before concrete EU market opportunities come up, will help you to make the right choices now in selecting your suppliers and ingredients, in developing your formulations, in deciding on your product positioning and claims, and in rolling out your EU sales and distribution channels.
This way you will avoid the need to switch suppliers, to adjust your formulations and/or to adjust the product claims potentially rendering it a very different (value) positioning. In addition, it will prepare you for questions about EU regulatory compliance and EU notification that potential buyers will surely have.