Just got a Surface Pro 4 out of the box, setup complete and Edge constantly displays:

Hmm, we can't reach this page

All other computers and devices in the house, PC and Apple work well.

Check for the in internet connection by hovering the mouse pointer on the desktop taskbar and check if there is any error. If the connection show internet access, I would recommend you to use Internet Explorer and check if it is working. If you any error, I recommend you to run network troubleshooter, it will automatically diagnose exact issue and try to fix it.

Press Windows + X keys on the keyboard and select Control Panel.

Type Troubleshooting in the search bar on the Control Panel.

Click on View all on the left navigation pane.

Click on Network troubleshooter.

Click on Advanced on the Network troubleshooter dialog box and click on Run as administrator (Enter the credentials if required).

Click on Next and follow onscreen instruction complete the Network troubleshooter.