If you are based outside the EU, you can elect whether you or your customer is the 'importer of record' [who the importer of the goods actually is and therefore who is responsible for the import charges]. If you make your customer the 'importer of record', your customer will be responsible for all import charges relating to the purchase. Many sellers experience large volumes of returns when shocked customers refuse to take delivery of their purchases because of unexpected import charges applied to the delivery of their item.
If you choose to be the 'importer of record' as the seller, rather than your customer, you should VAT register in the first European country where your goods land. Thereafter, selling into Europe will be subject to the same distance selling VAT Registration Thresholds as those companies already based in Europe.
The non-EU online retailers who are voluntarily registering for VAT, experience a big fall in returns and give their customers a much better buying experience.