Old furnace with no "C" terminal for wifi thermostat
The O terminal is C in your system

Because we know the black wire going off to the air conditioner is our Y wire (as it's connected to the black wire from the thermostat's Y terminal, according to what you have said and the photo's so far), the remaining wire in that cable must be a C wire, since you mentioned that there are only two wires going off to the outdoor unit.  So, we follow that wire to where it nuts in with the white wire going off to the O terminal and the brown wire off to the rest of the furnace, and that is the point where we tap C at.  Or in other words, in your system, O is what they call what the rest of us call C.