How do I use WPS to set up a network printer

We have an old wireless printer that doesn't have a screen, only a WPS button for wireless setup. There is no WPS on the T-Mobile gateways, so we used to work around.

Found an old wireless router sitting in storage that has WPS button. Programmed the old router with the same Wi-Fi name and password as the T-Mobile Gateway. Set up the printer to the old router using the WPS buttons on both. Then unplug the old router. The printer will automatically connect with the T-Mobile Gateway in the future.

Unfortunately, there is no WPS service on the T-Mobile gateway, or at least the one I have. For the record, I received the Arcadyan KVD21 5G gateway.

What I did (Kinda simple)

I didn't create a network. I just uninstalled the HP Smart App from my PC (Deskjet 2600 printer).

Installed the app again and it found the printer and added to the router (or network).

I checked the TMobile app on my phone and it shows connected. After that, I was able to add my printer to other devices. 

Note: Can someone try to delete the printer from their app first then try adding again. Just curious if it is necessary to uninstall then re-install the printer apps. This will also save others time and streamline the process. Let us know.