It took me a couple hours of trying to get their site to work so figured it would be helpful to post how I got it to work.
The webpage wouldn't let me use the purchase without registering option. It wouldn't let you click on that option.
I was unable to registering with Trenitalia with an address that is not Italy. I tried many things and couldn't get around not having a VAT / Tax Code. It gave the message Error code: 99 Tax code wrong.
After several hours of trying different things. I tried it in a different browser (Google Chrome). It worked right away.
Apparently the Trenitalia website does not work properly with Microsoft Edge.
Hopefully this post will save some people the frustration I went through.
p.s. - Have a good trip!