macbook air late 2010. no back up or restore capability. how to install osx Sierra from the beginning

Start here: How to reinstall macOS from macOS Recovery - Apple Support. See the section on "Other ways to install macOS."

i reinstalled Mountain lion from a time machine backed up Thursday.

i you situation, you need to factory reset the macbook air.

press option while restarting and select restart with my original OSX-sbow leopard.

if you can get a copy of that snow leopard usb that will work as well

then you can build up to what ever OSX you can find.

i hope this helps!