No C wire on furnace
Cut the red wire going to the A/C, strip the cut ends, and nut the C wire in with them

As it turns out, since you have central air conditioning, finding your C wire isn't that hard after all.  We start with the yellow Y wire from your thermostat, which is connected to the white wire in the cable going off to your condenser (outdoor unit).  From that, since we know that there must be a complete circuit going from the transformer (R wire), through the thermostat to the yellow Y wire, then through the compressor contactor's coil in the outdoor unit, and back to the transformer in the furnace in order for the air conditioning to work when called for, we can infer that the other wire (the red wire) in the cable to the outdoor unit goes to C; in this case, that's a terminal on your furnace's gas valve, which is corroborated by the air conditioner connections shown on your furnace.

As a result of all that, we can treat that red wire as a C wire; however, I'm not sure if you can have multiple wires to a terminal on that gas valve of yours (beyond what's already being done that is), so we need to cut that red wire in two somewhere in the middle, strip both cut ends, and wirenut the blue wire from the thermostat in with the two cut ends to gain access to C on your furnace.