In case the pickup signature hasn't been marked while in the pickup, the Help section on the app allows you to start the trip manually.
Please see screenshots below to see where you can mark the delivery as picked yourself in the app:
Click on the pickup task and open the task page. Validate as normal.
For SFS deliveries, all you need to do is inform the client store manager that you have arrived and turn your auto-accept on to receive automatically new orders!