Do I need an exhaust fan for my 2x2x4 tent?

I have the same issue, during the beginning stages, I don't run the fans much, I have it turn on for 15min every hour as that is the lowest my timer allows for. This allows for the humidity to build up but still try to flush out the hot air and I set the humidifier to 70% so it shuts off automatically. Also I keep extra pots in the tent with plain medium that I water (soaked) to increase the humidity in the tent. It would be ideal to have it hooked up like the infinity fans are designed to accommodate temp and heat with fan speed . but those are expensive.

The exhaust is important to replace the air in the grow tent it is not just for the smell although this is a benefit. Your plants at the stge they are at do not need extraction running atm. More important is to get your VPD correct which means increasing your RH by at least 20% from 40 to 60. Make sure you have air movement in the tent with a oscillating fan of some sort. 40% is too low for 2nd week. I personally run 70% RH at this stage but my extrctor would suck that out the room. No extractor yet but yes for flower.. Increase RH and balance leaf temp to get a VPD of around 0.80KPa (22ishc - 70%RH) ood luck and have fun..

I don't even HAVE an exhaust fan in my 2x4x6 tent! And especially at the age your plant is, I think it's more important to be concerned about the humidity level than eliminating odors or worrying about VDP (I really don't even know the first thing about VDP either!!). The little one needs the humidity - Good luck!