If you can’t see anything as you say (you don’t say what car model and engine so this does not apply to Duratecs etc) but if your water pump is fan belt driven take the belt off and start the car as it won’t hurt for a few min. Has the noise gone? If so it’s in the water pump or alternator area ( also it’s not unknown for the he cooling fan on the alternator to get one blade bent and touch where it can’t be seen). At least this way you narrow the search area.

BR Colin
Who used to be a Spanner Juggler