AF Amp circuit operation

Q4 is a preamp.
Q3 is a phase splitter.
Q1 and Q2 are a push-push amplifier.
* connecting a center tapped transformer in the output circuit would produce a push-pull amplifier. This is how I was taught 50 years ago. Today the terminology may have changed?
Anyway the key is Q1 and Q2 bases are being driven out of phase. Q1 and Q2 operating class B (conducting 50% of the time) feed the load a full cycle with one transistor biased off while the other conducts. (or AB with one being throttled down while the other is driven harder.)

When Q2 is driven into conduction current flows DOWN thru C1 and R3 to ground. Charging C1.
When Q1 is driven into conduction current flows from C1 DOWN thru Q1 to ground and UP from ground thru R3. Discharging C1.

Here we see the phase relationship between the signals.

The one thing to watch here is not to use to small a capacitor. A large capacitor will receive a large charge and provide the power on the next half cycle.

I set R1 and R2 to 4 Ohms with C1 at 1000ufd. 5ma battery drain and 180mv output with the same input as before.
It is a good earbud driver as I made mine but you can adjust the bias and add more power as desired.
Good luck!