If you install the door (with air gap), the smoke will vent out the chimney and not out the front. Once the wood burns down to hot coals, there won't be any more smoke and you can safely leave the door off.
I know this because when I used my oven for the first time last week, we had the door off and I noticed black soot forming on the exterior above the door opening. I took a wet paper towel and wiped off the soot, then installed the door (sufficiently cracked to allow ventilation) and immediately noticed that all of the smoke was now venting through the chimney. After the oven got up to temperature, we used the oven both with and without the door and no more soot.