Auto Click a Print System Pop Up Window

We have a software product that sends prints to a printer driver with the driver settings pre-saved to a file and applied at the time of printing. For reasons outside the scope of this question in some specific cases we need to open a pop up window for the OEM driver for the settings to be accepted by the OEM driver. In these cases the user has to click "Print" a second time, not ideal.

Our dev team is having a difficult time automatically clicking that second Print button so the user doesn't have to. The goal is the window would pop up for a fraction of a second and the file is sent off right away with only one click by the user.

I have personally tried playing around with AppleScript to accomplish this but have not been able to do so.

The application itself is written with QT and here is the info regarding the button in question from Accessibility Inspector:

Does anyone have any knowledge how to auto press this button?