MacBook Air 2013 with circle slash while trying to install Mojave
Updater didn't find a previous OS X install.


  Technical requirements:
  
  
  OS X 10.8 or later
  2 GB of memory
  15 GB of available storage to perform upgrade
  Some features require an Apple ID
  Some features require internet access
  
  
  Mac Hardware requirements:
  
  
  MacBook: Early-2015 or newer
  MacBook Pro: Mid-2012 or newer
  MacBook Air: Mid-2012 or newer
  Mac Mini: Late-2012 or newer
  iMac: Late-2012 or newer
  iMac Pro: Late-2017 or newer
  Mac Pro: Late-2013 or newer, mid-2010 and mid-2012 models with recommended Metal-capable GPU
  


What caught my attention was the
requirement for OS X 10.8 or later. Which (to me) indicates that a previous Mac OS X version needs to already be installed.
So if I were you, I'd probably get my hands on a copy of Mountain Lion, and install that first. Then attempt to install Mojave from there.

While you indicate yours is 2013, if it does turn out to be matter of your hardware being too old. Do note, that the OS Installer has a white, or blacklist that it consults to determine whether the hardware is an actual candidate for install/upgrade. I used to know where this file (.kext) was
located. But have since forgotten. A search on the internet should quickly reveal the location of the .kext file. Good sources for this information are in Hackintosh venues. :)

In case you didn't already know, and are interested. You can easily make a (USB stick) installer in the following fashion:

sudo /Applications/Install\ macOS\ Mojave.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume


where /Volumes/MyVolume should point to your USB stick (formatted with a GUID Partition Map and Mac OS Extended (Journaled) )

Good luck!