If you can access the pushbutton on the wall controller (you will need to open the enclosure of the wall controller to access the two pins of the pushbutton), you can solder two wires onto the pushbutton pins. That way, the relay click on OpenGarage will simulate pressing the pushbutton.
This is how we make the Security+ 2.0 adapter — we buy off-the-shelf Security+ 2.0 door buttons, and and solder two wires onto the pushbutton, and connect these two wires to the orange terminal block on OpenGarage.
Note that many pushbuttons have four pins, however, it’s really just two pins (the two pins on the same horizontal line are internally wired together and hence count as 1 pin). The easiest way to check is to use a multimeter to check the connectivity. When button is released, the two pins appear as open circuit; when the button is clicked, the two pins appear as short circuit.