Some contributors here will say that each account has to be associated with a unique number. For precisely the scenario you are mentioning I do not see why Apple would require that. I suggest you contact Apple and ask them what to do. If they provide a solution then please report back here with it.
This support article has various country telephone numbers for contacting Apple for support and service ➔ Contact Apple Support - Apple Support Scroll down to “Connect with live support”. If your country is not in the list, go to the “Other countries” entry at the end of the list. Not every country has telephone support, and phone numbers may only work when calling from the same country.
For chat, you can try using the Apple Support App —> https://apps.apple.com/app/apple-support/id1130498044
For chat help with a USA Apple Account —>
https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0998&symptom_id=20198
If in the end you are required to provide a number, see if you can find somebody who does not use Apple equipment who would let you borrow their phone for a short while so you can sign up. This is probably for two factor authentication and once you have signed up there are other ways you can get verification codes (which you seldom need). Get a verification code and sign in with two-factor authentication - Apple Support