If you don't trust them, take it to another shop for confirmation. here is a guide so you can look at the leak yourself to confirm the water pump:
https://www.2carpros.com/articles/car-is-leaking-coolant
I can tell you the water pump and timing belt failure is common.
Water Pump, R&R 3.0 HRS @ shop rate. Look on amazon for the parts prices.
Here is how the job is done. in the images below. Check out the images (below). Please let us know what happens.
Images (Click to make bigger)
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Thursday, August 3rd, 2023 AT 1:42 PM