You have some sort of leak, no question about it. The leak can be coming from only three places: 1) the drain pipes; 2) the supply pipes; and 3) from the faucets or sink surround from above the sink itself.
Put a stopper in the drain and run water into the sink. If it leaks, you have a leak from above. If there is no leak, turn of the faucets and let the water run through the drain. If it leaks then, you have a drain leak. If it leaks when the faucets are turned off and there is no water in the sink (i.e., if it leaks “all the time”), you have a leak in the supply fittings to the faucet.
As you can see, the diagnosis of plumbing problems is extremely logical.