So it makes this noise when parked next to a wall on start up AND not moving? Then its something in your brake pads/calipers. The parking brake operates brake shoes inside the rotor. The hand brake is separate from the car's braking system.
Taking a wild guess I'd say your new brake pads are moving in the caliper. Or maybe they didn't have heat shields/pads to dampen pad noise. You can also use some ceramic brake pad lube on the caliper where it contacts the pad backing pad. You used new spring clips on the pads right ?
Or maybe it's as simple as a loose brake caliper bolt ?
Maybe post a video of the noise.
