If I live in UK can I register a business in EU and sell on AmazonEU?

I live in UK. I’ve never sold on Amazon before. I have a really good idea for a private label supplement.

I’m thinking my options are :

UK manufactured product. Sell on Amazon UK. UK business EU manufactured product. Sell on Amazon EU. EU business ??? USA manufactured product. Sell on Amazon USA. USA business ???

For EU or USA I guess I’d be paid in Euro & Dollars, so would have to convert it to GBP if I wanted to spend in the UK.

Is it really that simple?
I’m thinking it might not be much harder to sell on EU than UK, but a much bigger market, so easier to sell all my stock quickly.

An EU registered business would get around Brexit taxes??

What are the extra costs of being UK based and selling on EU and USA?

Or start off small in the UK then expand to EU & USA afterwards?