https://developers.facebook.com/docs/sharing/domain-verification
and
https://www.facebook.com/business/help/286768115176155?id=199156230960298
"Who is Domain Verification for?
Domain Verification is the best way to handle ownership if:
- You have the ability to upload HTML files to the web root directory or the ability to edit DNS TXT records"
I don't think you're going to be able to use itch.io for that, you need to purchase a domain and get webhosting, I recommend GoDaddy because for fresh accounts the first year is $1 (if they still do it) then for hosting you can get a free one at 000webhost, once you have both change the nameservers on the domain to the ones you have from 000webhost.
Then you can either upload the HTML file or add a TXT record on your DNS (probably easier to just do the HTML file) with an FTP software, Filezilla should do it just fine.