it’s due to the pressure in your lines. the pressure is being reduced at the faucet causing a water hammer. If you have a well system you can turn the pressure down on your pressure tank, If it’s city water then you may need a pressure reducing valve where the line comes into the house.

I’m familiar with a thumping or bumping noise in water piping when opened, running faucets are quickly CLOSED. It’s called ‘water hammer’. It’s caused by the sudden stopping of the flow of the water — causing it to ‘bang its head’ against the closed valve. I was first aware of such a ‘phenomenon’ when I drew water from a deep water well system that had a very long run of piping from the pressure tank to the faucet I was using. It made a kind of clanging-knocking sound — sometimes more than three times — and I could feel the first and hardest knock through the ground under my foot (the piping wasn’t buried very deep).

YOUR thumping noises in your cold water system when the faucet (tap) is turned on probably is caused by air bubbles passing through the fittings in your piping system. If the air bubbles are large enough and numerous enough they should cause some spitting and spewing as they come out of the tap.

thumps when you turn it on
simple
most likely a loose washer

Joe R is 100% correct. Maybe even 110%.