Using a relay to "push" a button upon starting v

My durango is equipped with electronic start/stop which turns off the vehicle at red lights etc (any stop more than a few seconds) I have a button on the dash that when pressed, lights up and turns off this feature... the only issue is, you have to hit this button every time you start the vehicle.   

Is there a way to use a relay so when I start my vehicle it "pushes" the button automatically, turning off the feature?

Seems like it'd be the same type setup that's used for bypassing "having your vehicle in park" for a screen.

Thanks in advance for your help!