Smart Thermostat - No C-Wire - No Controller Board
n here]1

This is a Heat Pump wiring diagram, if you only have an AC unit then the AC unit outdoors will only require the Yellow and the Common wire as far as the 24 volt control circuits go.
Common is the side of the 24 volt control circuit that every 24 volt circuit returns to, to complete the circuit, this is why it is called Common,  cause every circuit terminates there.
Every 24 volt device has a 24 volt hot leg  and a Common,  the AC unit will have the Yellow 24 volt hot leg of power  and the Common side of the 24 volt control power.

The furnace or air handler has  low voltage terminals R/ red, W/ white, Y/ yellow,
G/ green and C/ common.
The circuit board will have them if no low voltage terminal strip is seen.
Follow the 24 volt wiring to see where the terminals are, the pics you gave show nothing of any use, its hiding the components, google 24 volt hvac transformer, or 40 VA HVAC transformer to see what one looks like.
Red is the 24 volt hot leg of power
White is the Heat circuit
Yellow is the Cool circuit
Green is the Fan on circuit
Common is the side of power every 24 volt circuit terminates upon.
1 of the 24 volt wires going to the AC unit will be Common.