NE555 delayed triggering
The AD_KEY signal goes to an analog to digital converter (ADC) input on the microprocessor.  The software reads the value from the ADC, then decides which button you pressed.  There will be a tolerance range around the voltage that the controller expects for each button, but it may be rather narrow.
I simulated your button-press transistor to see what voltage AD_KEY should get for your button:



simulate this circuit &ndash; Schematic created using CircuitLab

If I replace Q1 with a short circuit, I get 1.245V for AD_KEY.
If R3 is 300k, then AD_KEY is 1.303V
if R3 is 1k , then AD_KEY is 1.250V

There's only 58 millivolts difference between the &quot;real button press&quot; and the 300k version, but maybe the processor is really that picky.  Try it with 1k for R3 and see if it works.
If that doesn't help, you may need to wait longer after startup before &quot;pressing the button.&quot;
The processor probably has some tasks that it does on startup, and may not see your button press correctly.  The processor might also be set up to ignore buttons that are pressed at power on.
Extend the delay by maybe a couple of seconds and see if that helps.