When I drive through a puddle of water the car makes a squeal noise maybe from a belt. It goes away after a minute.

Verify belt to pump ..is belt glazed or cracked....run engine have assistant in park turn steering when noise is audible pour water on belt if it goes away squeal you need a new belt

Sounds like one of your pulleys is bad. Alternator, water pump, don't know till you find it. You say you have more than one belt-try taking one off at a time, run engine for a couple of minutes and see if squealing goes away. Maybe you can isolate it that way.
If belts are off, you could spin each pulley by hand to see if you could catch the one that is bad. Any little wobble or play in any of the pulleys would be very suspect as the likely bad one.

Your water pump may need a lubricant. Water pump lubricant is added to the radiator.
When the weather is warm enough, and the engine runs hotter, then the thermostat opens more frequently, the lubricant will mix with the radiator fluid and circulate through the sysem lubricating the water pump.
I had squealing problem after changing the serpentine belt.
Tried changing idler sprocket, no difference.
I added the lubricant to the radiator, unfortunately the weather was cold, and the lubricant did not mix well with the radiator fluid, and did not circulate well do to cold weather and short drives.
Once the weather got warmer and the thermostat opened more often the squealing stopped.

You did not give the make model and year, and I did not get all of the story.
Are you saying the noise goes away when the ac is on, or off ?

The squeal is coming from the alternator belt, When the temp is low, the belt is hard and glazed and lost its ability to create friction.

It sounds like your water pump is going it usually vibrates throughout everything if it was your alternator it would show signs with your power the easiest way would to take your belt off remembering the belt route and spin the alternator pulley and the water pump pulley to see if they spin freely without noise

It does sound like a belt, you might try an inexpensive can of belt treatment to see if it helps. Later you might want to replace the belt.

Seems like a drive belt problem, to confirm pour some water on belts the noise should go away or may get louder for a second. If either happens the belt or belts needs to be adjusted or replaced. Good Luck, If I fixed ya, leave me a FIX-YA comment thanks

its your engine belts need to change them. have a nice day

Belts stretch from new. Try to tighten them again. Hopefully the are not glazed or this may stay with you.