Earlier quoted context omitted.
You can block the YouTube domains on pie hole or with something like OpenDNS.
I did that and then my 10-year-old installed a vpn extension on his Chromebook.
It's always a cat and mouse game, and was when we were kids too.
You can (in order of simplicity):
* Get a list of common VPN provider domains and block in DNS
* Block all traffic to common DNS ports
* Use various filtering/monitoring applications to categorise traffic and look for odd outliers (probably VPNs)
* Force proxy only access and MITM sniff traffic
Of course the most important thing to do is discuss consequences and bring up why it's hurtful for him to lie to you via his actions. But the above technical solutions will cover 95% of what most kids can do... Until they can get a mobile data connection.