Mac Book Air 2017 compatibility

That Apple Support document describe a couple options, but they are for newer Macs with USB-C ports: Adapters for the Thunderbolt 4, Thunderbolt 3, or USB-C port on your Mac - Apple Support.

Your Mac does not have an HDMI port. You would need to find an equivalent for the Thunderbolt port on your MacBook Air: Identify the ports on your Mac - Apple Support.

The inability for that monitor to recognize the Mac is most likely an incompatible adapter. You need to find one to convert Thunderbolt digital video to VGA. There are many inexpensive ones. I don't have any particular recommendations.

There are an enormous selection of compatible monitors: Use an external display with your MacBook Air - Apple Support

Are you serious about using VGA though? Its resolution is awful compared with what you can accomplish with HDMI, and you would need to purchase an adapter, but you can certainly do that.