I've given your thread a meaningful title.
Q3 is upside down in your schematic.
Your output is shorted to ground.
Your power supply polarity is wrong backwards.
You should use driver transistors to provide high current base drive to your output transistors.
If you want to avoid "crossover distortion" there should be an offset voltage between the bases.
You can generate a square wave with an oscillator such as a 555.
If you need controlled and straight sides, you can use current sources and a capacitor.
Tell us IN DETAIL about the WHOLE project then we may be able to suggest something.