You really need to create a bootable OS installer with the last supported version of OS this system can support which is macOS High Sierra (10.13.6)
So from a working Mac system format a 32GB thumb drive with GUID and HFS+ file system, then download from here [https://support.apple.com/en-us/HT211683|How to download and install macOS] putting in onto the thumb drive. Then follow this to convert it to a bootable installer [https://support.apple.com/en-us/HT201372|Create a bootable installer for macOS]. Now with this in hand plug it into your MacBook Air system wipe the drive using Disk Utility from within it and then install a fresh copy of the OS.
That should do it!