screechy brakes

What does "mechanic tinkered with the brakes a few weeks ago" mean? What did the mechanic do? Why? Did you take the car to the mechanic because you were having brake problems?

Your problem has nothing to do with the engine being cold. It's most likely nothing more complicated than the pads having set on the rotors overnight. That is very common in a large number of cars. Cheap pads are more prone to this than a decent set of ceramic pads. If the mechanic replaced your pads as part of the "tinkering", then it would be worth finding out what kind of pads were used to replace yours, and whether the mechanic installed the shims behind the new pads when he installed them.

The reason they stop making noise after you apply them is that any slight rust that begins overnight, or any slight set that the pads take to the rotor overnight, is eliminated by applying the brakes. The pads are pushed into the rotors, aligning them flatly against the rotors, and preventing them from oscillating, and any buildup on the rotors is scraped off, allowing for a complete contact area between the rotor and pad - again resulting in eliminating any oscillations.