Arm Stay without Entry/Exit delay

Yes, you can do this with the No Entry Delay option available whenever arming on the panel or in the Alarm.com website or App.

On the panel tap the arrow on the right side of the arming card to bring up the additional options like turning off entry delay.

You can also create a scene in Alarm.com that arms the panel stay with no entry delay, then run the scene from the app or the panel.