You don't have to exhaust the air outside. You can just have a fan and filter exhausting the tent air into the room. You'll still need a way to manage temps, but with LEDs, it's much less of a challenge.
Trying to blow air into the tent, through a microfilter is very inefficient. You'll have to run your fan much faster than normal, which adds heat from the fan to the room.
You really only need to have the filter connected from about the 3rd or 4th week of flower. There won't be any odors before then. If smell is of a concern, you might want to get a room air purifier, as well as the inline fan and filter. Using the fan the way you have it set up, and without a carbon scrubber, you will accumulate so much smell in your residence, that it will be detectable from several houses away.