I understand you want to install macOS 10.12 Sierra on a mid-2013 MBA. The good news is that it will run on that Mac. The "bootable installer" (presumably a USB flash drive) would be the best option, but I understand it's not working for some reason. You would be better off making that option work.
Lacking a bootable installer, boot macOS Recovery and choose "Install macOS"
Intro to macOS Recovery - Apple Support
You may need to choose macOS Internet Recovery, otherwise Recovery will offer the latest compatible macOS version, which that Mac is already using.
To force Internet Recovery:
- Option-Shift-Command-R: Start up from macOS Recovery over the internet. Use this key combination to reinstall the version of macOS that came with your Mac or the closest version that's still available.
When asked where you would like to install it, choose the external device. Then, upgrade it to the macOS version you need: How to get old versions of macOS - Apple Support.
... can't seem to make it bootable, much less w/ version 10.6.
That Mac will not boot OS 10.6 "Snow Leopard". The last Macs that could were 2011 models, so yours is too new.