Does your USB to serial converter (CH340) have a DTR output? If so, connect the DTR output from the USB to serial converter to the reset pin on the Pro Mini through a 0.1uF capacitor.

You should be able to upload without pushing the reset button.
Does your USB to serial converter (CH340) have a DTR output? If so, connect the DTR output from the USB to serial converter to the reset pin on the Pro Mini through a 0.1uF capacitor.

You should be able to upload without pushing the reset button.