You can use any provider you want, those are just recommendations.
First, manually create a database. You can usually create it via the console. This is an example for the Google Cloud SQL provider:
Temporarily change the backend/.env database credentials to point to this database.
On the backend, run:
npm run db:create
Now revert the database credentials to the localhost ones.
Cloud database providers usually start the database blocking all external connections. You must whitelist the IPs you will use.
In case you want to allow all IPs, the pattern is usually 0.0.0.0/0.