Would it be possible to use Guacamole in a setup with a server and a client, if neither the server or the client has an externally visible IP, and their firewalls cannot be configured?

Alternatively, are there other solutions which make it "easy" to enable SSH access to the server in such a scenario?

Gravitational Teleport[0] is exactly what you've just imagined.

I set up the free version a few month ago. if that suffices, its really neat.

if it doesn't... the paid version probably still won't be an option, because it's silly expensive.

[0] https://github.com/gravitational/teleport