Hi Squires Misses,
Congratulations on your new MacBook Air. For help with signing in to your Apple ID, test the sign in on a different Wi-Fi network. If your Mac isn't connecting to the internet over Wi-Fi
If the issue continues, ensure your macOS software is up to date. The steps here can assist: Update macOS on Mac
Once updated, test the sign in once again with the steps below found in the article here: Sign in with your Apple ID - Apple Support
"Sign in on your Mac
- Choose Apple menu > System Settings. In earlier versions of macOS, choose Apple menu > System Preferences.
- From the sidebar, click Sign In with your Apple ID. In earlier versions of macOS, click Sign In.

- Enter your Apple ID and password.
- If prompted, enter the six-digit verification code sent to your trusted device or phone number and complete sign in."
If the issue remains, reach out to Apple Support directly to ensure you can sign in on your new MacBook Air.
Contact - Official Apple Support
Contact Apple for support and service - Apple Support
Best.