The olfactory nerve extends directly from the brain. It is the first cranial nerve pair.
https://en.wikipedia.org/wiki/Cranial_nerves
The nerve forms a bulb directly above the nasal cavity. That bulb emits many smaller projections through the skull and into the nasal cavity.
https://en.wikipedia.org/wiki/Cribriform_plate
https://en.wikipedia.org/wiki/Olfactory_foramina
The nerves pass through those holes in the bone which are called olfactory foramina. Foramen means hole and these foramina connect the cranial cavity to the nasal cavity.
The paranasal sinuses are nearby structures. The olfactory nerves do not go in there.
It's absolutely a fact that the nose is pretty much directly connected to the brain though. The best demonstration of this fact is naegleriasis:
https://en.wikipedia.org/wiki/Naegleria_fowleri
https://en.wikipedia.org/wiki/Naegleriasis
This thing lives in water. If that water enters your nasal cavity, it will travel via olfactory nerve to your brain where it will proceed to literally eat it.