Sorry, you need a physical remote. There's no way to get a Roku TV connected to Wi-Fi without one and you can't use the app until it's connected. You can see if your remote is transmitting anything by pointing it at a digital camera like the one in your phone. You should see flashes coming from the remote on the camera's screen when you press buttons on the remote.
You can get a Roku simple TV remote or most universal remotes support Roku TVs.
Roku TV Remote | Replacement Remote For Roku TV | Roku
Roku Community Streaming Expert
Help others find this answer and click "Accept as Solution."
If you appreciate my answer, maybe give me a Kudo.
I am not a Roku employee.