How do I determine where to connect a new C wire inside my furnace when no control panel or wiring terminal exists?
You will need to connect the blue wire for "C" to the wiring node that corresponds to the "BL" connections at the transformer as indicated by the yellow highlight in the following picture. 

Do not connect to those two white wires unless you first confirm that the also connect into the "BL" node at the transformer.



Note from the picture that this "BL" node is also connected to the ground connection of the furnace. This is most likely the metal frame of the furnace so you could look also for a screw that attaches to the metal frame and attach your blue wire there.