I don't know if it's related but for some reason after the release of the 1.0 Galaxy removed the start menu shortcut from my installation.
Maybe it's something wrong with how Galaxy tries to create/update the shortcut since the main .exe for the game changed it's name from the InDev version to the released one (previously it was called CrossCode-beta.exe and now it's CrossCode.exe)
In the meantime, if you want to create a desktop shortcut you can do it manually from the game's folder.
If you are using galaxy, press the more button/ manage installation/ show folder, this will open the game folder and you can create the shorcut from there drag the CrossCode.exe with the right button to the desktop. (instructions just in case you don't know how this work)
The only think is that this shorcut will not launch galaxy when you play the game, so it wouldn't save the time played.