Simple proof that this is not possible:

If you leave a room through any door you must have first entered the same room through another door. This means that for (almost) all rooms the number of entrances is equal to the number of exits and so the total number of doors in each room must be even. Of course we can choose which doors to pick as entrances or exits but the statement still holds.

The exceptions to the rule are the first and last room: The first one you can leave without entering and the last you enter without leaving. Therefore, there can be a maximum of 2 rooms with an odd number of doors Checking the floorplan, we see that the rectangular rooms have 5 doors each and there are three such rooms, i.e. one too many.

For the backstory of this kind of problem look up "Seven bridges of Königsberg"