Quake/Tilda style in ConEmu
ConEmu may pull down from the top of the screen like gaming consoles do.
Quake style drop-down may be enabled/disabled on the Appearance Settings page.
There are some options for it like ‘Animation time’ or ‘Auto-hide on focus lose’.
And of course you may choose desired global hotkey. Look at Keys & Macro Settings page and set one or both ‘Minimize/Restore …’ hotkey.
Do you want to start ConEmu hidden?
Check out ConEmu.exe command line switches,
especially /StartTSA
.