The map editor for Ashes of the Singularity is available, but not enabled by default in the current build. You can enable it by doing the following:

1. Go to the install directory for AotS
2. Navigate to Assets > UI > FrontEnd, and open MainMenu.xml in a text editor
3. Look for the line '<Button ID="MapEditor" Anchor="L,C" Style="MainMenuButton" String="MAP EDITOR" Hidden="1" />'
4. Change Hidden="1" to Hidden="0", and launch AotS. A new main menu option, "MAP EDITOR", will now be available.

Note: These changes will be overridden whenever a new build is released.

Pictures: https://forums.ashesofthesingularity.com/467525/page/1/#3567757

With thanks to Sargeras77 for confirming this works.