When embroidering hats the logo can only be 2.1″ tall. The reason is the embroidery machine hoop needs space at the bottom and top to attach the hat.
The reason you may see some brands like MLB baseball hats having such a large logo is those hats are embroidered flatt and then constructed after the logo is embroidered.
If you want something like that we can definitely help with custom hats. Typically they require 5-6 weeks and a minimum quantity of 48.