OS X Install Disk not showing

FYI, there is no 2016 MBAir. You either have a 2015 or a 2017 model. Fortunately both models are nearly identical so not really an issue here, but since you are installing macOS 10.11 it means you actually have the 2015 model.

If you had macOS 10.13+ installed previously, then you will need to use Disk Utility to completely erase the physical drive as GUID partition and MacOS Extended (Journaled).

If this laptop is using a third party SSD, then you will need to boot into a macOS 10.13+ installer. You can try accessing the online macOS installer by booting into Internet Recovery Mode using Command + Option + R. Unfortunately some Macs will only boot to the oldest online installer compatible with their Mac for the OS which originally shipped on the Mac from the factory. If this happens, then you can create a bootable macOS 10.13+ USB installer using the instructions in this Apple article:

How to create a bootable installer for macOS - Apple Support

Creating a bootable macOS USB installer does require access to another Qualifying Mac. A Qualifying Mac is one which is compatible with the OS installer you want to download. For example, to create a bootable macOS 10.13 installer requires a Mac from 2010 to 2018 (or even some Late-2009 models). While a macOS 12.x installer requires access to a Mac from 2015 to 2022. You can use the information in this article to determine a Qualifying Mac since it shows which versions of macOS are compatible with various Apple hardware:

https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

With macOS 10.13+ you may need to click "View" within Disk Utility and select "Show All Devices" so that the physical drive appears on the left pane of Disk Utility.

FYI, if you just installed a third party NVMe SSD, then besides needing to use macOS 10.13+, you also must have previously had macOS 10.13+ installed while the original Apple OEM SSD was installed so that the laptop's system firmware has already been updated to work with an NVMe SSD. You will need an original Apple OEM SSD for this specific laptop to use temporarily in order to install macOS 10.13+ which will then update the system firmware so that the new NVMe SSD can be used.

If the laptop has the original Apple SSD and these instructions don't help to see the physical SSD, then the SSD has most likely failed. You can either have Apple repair the laptop (expensive), or you can replace the SSD with a third party SSD assuming the laptop at one time had the system firmware updated by the installation of macOS 10.13+.

If the laptop has a third party SSD and these suggestions don't allow you to see the physical SSD, then it most likely means the SSD is bad or possibly the SSD adapter if using an M.2 SSD.