Subdomains are getting a 403 forbidden error when inside public_html

I created two domains for testing:
sub1.site.com
sub2.site.com

sub1’s directory path wasn’t provided, its living inside the main root folder, and visiting the domain works - shows the default index.html

sub2’s directory was specified as public_html/sub2.site.com . Visiting it I receive a 403 Forbidden error.

I’m unsure, but I add this record to my domain registrar many hours ago:

HOSTNAME ||| TYPE ||| ADDRESS
*(asterisk) ||| CNAME ||| [my-site-url]

Tho it still didn’t sort out… sub2 is is still getting error

What must I do?

Secondly, I have reserached the internet on this part, but would it be any benefit to keep it as it is (subdomain’s folders being outside public_html) other than “its just a directory”?