The OLED displays have exposed contacts on the rear side.
It is crucial to apply electrical tape on the backside of the OLED display to prevent shorts between it and the Pro Micro. Any insulating tape will suffice.
There will barely be enough space on the header pins to fit the OLED display, but it’ll still fit. Solder one pin first, and then fix the alignment of the display while keeping the single pin warm. Once you’re satisfied, allow the pin to cool down and solder the remaining pins in place.
By soldering only one pin, you can more easily adjust the angle and alignment of the OLED display. To readjust, simply reheat the pin, move the display, and let it cool down again. Once you're happy, solder the rest of the pins.
There won’t be much solder connecting the pins on the back, but it is enough for a stable connection.