Looking for VAT advice (Milan)

Hi all,
I have recently started my own business in the USA. The products are designed by me, and made by a factory here in Italy to be sold around the world (but are not currently sold anywhere...I am in the development stage). The factory recently asked me for my VAT number, which we do not use in the USA, so he can send an invoice.

Am I required to get a VAT number here in Italy? If so, what is the process?

Thanks for your help!
Stephanie