How do I assign the cars that are supposed to bring asphalt for the paver? I searched everything and found nothing.

The paving crew was available from game start, but Captain of Industry hides its Assigned trucks controls behind the later Custom Routes research. So there genuinely was no assignment button to find.
This is fixed in v0.12.7. Select the MZ Asphalt Paving Crew, open Assigned trucks, then use the + buttons to add loose-material haul trucks and an MZ Asphalt Paver. Haulers carry asphalt from the plant to the crew, and the paver carries it from the crew to the road.