OSX Installation to MBA (Macbook Air Model A1370) SSD upgrade
Unfortunately, it is not possible to install an M.2 SSD into a MacBook Air (or Pro), because Apple SSDs aren't M.2, and (please correct me if I'm wrong) there are no Apple SSD to M.2 adapters, partially because (this is what I've been told) an M.2 SSD has to be directly mounted to the motherboard. Also, it's quite possible that M.2 SSDs are different dimensions than an Apple SSD, and might not fit in the (computer's) case.

You can however buy an Apple SSD from OWC, which should work perfectly with your MacBook Air.