What causes a loud screeching noise when central AC turns on?

The first thing to check is whether your system actually has a fan belt. Unless your AC is a very old model or a commercial unit, it is almost certainly a direct-drive system. Residential air handlers built in the last few decades do not use belts.

If you do happen to have an older belt-driven unit, a slipping belt usually sounds like a high-pitched squeal, very similar to a loose fan belt on a car. It happens at startup because the motor gets up to speed instantly while the heavy fan takes a moment to catch up.

However, your description of a "brutal metallic grinding" that only lasts for 10 seconds points to a different, very specific problem.

It is unlikely to be the blower motor bearings. When bearings fail, they usually make a continuous rumbling, squeaking, or grinding noise the entire time the fan is running. They do not typically grind for 10 seconds and then suddenly go quiet.

The most likely culprit for a harsh, temporary metallic grind at startup is a loose blower wheel.

Inside that unit above your ceiling is a large cylindrical fan called a squirrel cage. It is attached to the motor shaft by a single set screw. If that screw backs out slightly, the motor shaft will spin wildly inside the metal hub of the fan when the AC kicks on. This creates a terrible metal-on-metal screech. Once the fan finally gets up to speed and catches, the noise stops.

Another possibility with a loose wheel is that the initial torque of the motor starting causes the wobbly fan to shift and scrape violently against its metal housing. Once it reaches full speed, centrifugal force stabilizes it and the scraping stops.

You can figure out exactly what is happening with a quick physical check.

First, turn off the power to the air handler at your main breaker panel. Do not skip this step, as the capacitor inside holds a charge and the motor could start unexpectedly.

Open the access panel on the unit above your ceiling. You will see the blower wheel inside its housing.

Reach in and try to spin the wheel by hand. If it feels stiff, or if you feel a rough, gritty resistance as it turns, your motor bearings are indeed shot and the motor will need to be replaced.

Next, hold the motor shaft still if you can reach it, and try to wiggle the blower wheel back and forth. If the wheel moves independently of the shaft, or if it wobbles side to side, the set screw is loose. You should also look around the bottom of the housing with a flashlight. If the wheel has been scraping the sides, you will see a pile of shiny metal shavings.

If it is just a loose set screw, you can often align it with the flat side of the motor shaft and tighten it down with a wrench. If it has been grinding for a while, the inside of the wheel hub or the motor shaft itself might be chewed up. If the metal is heavily damaged, tightening the screw will not hold for long, and you will likely need to replace the blower wheel.