Hello.

I am trying to use remote debugging for the first time, but it wont start.

I have installed the required extension on the server, and dbg-wizard.php tells me that everything is all right.

I suspect that the problem is that port 7869 is closed in the firewall at the hosting center where my server is located. Can I use another port instead? (I know that port 443 is open)

Thanks.

Do you mean 443 is open for the outbound connections? In this case, it's useful and you can change port in the debugger settings.
FYI, in most cases it's not server firwall blocks outbound connections, it's your own router on the client side does not know where to forward inbound connections to. If it's NAT router, you can set port forwarding. Otherwise try using ssh tunnel.