I think the mistake the OP made was going to unifi.com for the setup, when in fact you can go to 192.168.1.1 and set it up fully locally from there.

The cloud management is great after setup, but not during setup because yeah you keep losing connection to it whenever you break the internet or whatever. This is greatly alleviated with their fancy 5G router they just released, which allows you to remote manage even if the internet is broken.