I don’t think its possible to do that without AWS Route 53. I think press has recently started supporting Cloudlfare, but I am not sure.
Otherwise, you can’t do that with out Route 53 unless you can make heavy configuration changes in press. Press is configured to work with Route 53. For multiple sites, Press automatically handles DNS configuration for all sites with wildcard.
You can use OCI with out issues. Follow this guide [Guide] Installing Press and get it up and running - Part 1