You should use the OD Cost Matrix solver and not the route solver. You can load all your 1960 departure locations as Origins and your 1 arrival location as the Destination and Solve. You will get an output line feature class with 1960 records. Do note that it will place a straight line between the locations but the computed distance will be over the network. If you also want to get the geometry of the actual path travelled then use the Closest Facility solver.
Read more about OD Cost Matrix here: