Some VECs require that their VE teams send the entire packet of paperwork back to the VEC's home office after a test session. Staffers at the VEC then review the paperwork and prepare a batch upload to the FCC for processing and license issuance. Given the time delay in sending the packet through the mail, reviewing the packet, and transmitting the data to the FCC, it might take a week for your license to be issued.
Other VECs push this processing off onto their VE teams. They expect the VE team to review the paperwork from the test session and upload a results file to the VEC. The VEC then merges each VE teams results file into a composite file that is uploaded to the FCC for processing and license issuance. This is how some VE teams are able to give a test on Saturday and have the new licenses appear in the FCC's database on Monday.
There is no method for an amateur radio licensee to apply directly to the FCC for a new or upgraded license. It must go through a VEC. OTOH, address changes and license renewals can be processed directly through the FCC's web site.