If Q1 is faster and has a higher gain than Q2 is will turn on first when you apply the input
power and will hold Q2 off. Load current and transformer magnetizing current then flows in the upper half of the primary winding, and auto transformer action supplies the base drive until the transformer saturates.
When that action occurs, Q1 loses its base drive. As it turns off, the transformer voltage reverse, turning Q2 on and repeating the cycle.
Circuit 12VDC to 110VAC Inverter
The output frequency depends on the transformer iron and input voltage but not on the load. The frequency range between 50 to 60 Hz with a 60-Hz transformer and car battery or equivalent source. The output voltage depends on turns ratio and the difference between input voltage and transistor saturation voltage. For higher power, use larger
transformers and transistors.