DIAGNOSIS
The setup process is failing at the Wi-Fi connection stage. This is often due to network incompatibility.
FIX
Use the 2.4 GHz band. The Echo Show 10 3rd Gen requires a 2.4 GHz Wi-Fi network for initial setup, even if your router broadcasts both 2.4 GHz and 5 GHz. Temporarily disable the 5 GHz band on your router, or ensure your phone is connected to the 2.4 GHz band before starting setup in the Alexa app.
IF THAT DIDN'T WORK
Restart the setup process completely. In the Alexa app, go to Devices > '+' > Add Device > Amazon Echo > Echo Show. When prompted, hold the Action button on your Echo Show 10 until the orange light ring appears to put it back in setup mode.
HEADS UP
Ensure your Wi-Fi password contains only standard alphanumeric characters. Special characters like &, %, or # can sometimes cause connection failures during setup. Use a simpler password temporarily for testing.