While working in an environment where VPN connections were pretty much all blocked⁰ a friend of mine had success using https://guacamole.apache.org/ to access a remote machine¹. Not quite the same as a direct VPN connection but worth a try if nothing else functions, it looks enough like normal HTTPS traffic that he got away with it.

To keep your wireguard setup more as-is, you could try https://kirill888.github.io/notes/wireguard-via-websocket/ to tunnel that via a web server. In fact https://github.com/erebe/wstunnel which that uses could be used just as well with any other UDP based VPN.

I once tinkered with https://github.com/yarrick/iodine and successfully connected to resources over the wireless on a train, bypassing its traffic capture and sign-up requirement, so that might be an option, though I think fully blocking external DNS is more common now so this is less likely to work²³.

[0] practically only HTTP(S) permitted, not even SSH, DPI in use that detected just using SSH or OpenVPN over port 443

[1] NOTE: be careful breaching restrictions like this, you are at risk of an insta-sacking if discovered, or worse if operating in some securiry environments!

[2] and the latency when it does work is significant!

[3] and that much traffic over port 53 might get noticed by the heuristics of data exfiltration scanner, encouraging sysadmins to notice and implement a way to block it