If this is a submersible pump, the problem is probably with the check valve(s). There should only be one check valve in the sytem, located right on top of the pump. If you have another check valve up top, remove it and the "thunk" will go away. Although the extra check valve maybe masking the real problem, which is your down hole check valve is out or leaking back, or a hole in the drop pipe. After removing the above ground check valve, if the pressure drops when no one is using water, you have a bad check or a leak in the pipe down hole.
A lot of people don't think an extra check valve in the system will hurt anything. But this is exactly what happens when when the bottom check fails or even leaks back a tiny amount. It is not if, but when this will happen. It is much more obvious on larger pump systems, but happens on all pump systems.
Another possiblity is that you have too much air in your bladder tank, and the bladder is hitting the bottom just as the pump starts. If this is the case the extra air didn't get in there by itself. It would mean the bladder in the tank is bad and the extra pressure is caused by the water getting on top of the diaphragm.