MacBook Air

A "-2003F" error code would indicate an issue with your network router not being able to provide a workable DNS server address to your Mac ... in order for it to locate the Apple servers to download macOS.

Try temporarily connecting your notebook directly to your router using an Ethernet cable instead of Wi-Fi.

Other reasons that you are having trouble with restoring your notebook would be:

• The wireless network is configured to use a hidden (non-broadcast) network name or SSID.
• The wireless network is secured with either WEP or WPA-Enterprise.
• The connection requires certificate-based authentication / 802.1x. That is, the connection requires authentication by a RADIUS server.
• The connection requires the use of Proxies (where specific proxy servers must be configured in network preferences)
• You are trying to connect to a Captive Wi-Fi network (where you click an “Agree” button to access the Internet)
• You are trying to connect a network that gets its Internet access via a PPPoE connection (where there is no router handling that connection type.)