Your brakes should not make noise, even when they are new. The only time they make noise is when the wear indicator touches the disk, when they are worn out.
Are they OEM, or are they jobber pads. I have bought jobber pads and had them make awful noise. I bought another make of jobber pads, and they worked fine. The pads should have a warrantee on them. If they do not, you got ripped off. The pads I buy have a lifetime (of the pads) warrantee.
Did you replace the rotors, or at least re-face them ? It is common practise now to replace them.
Did noise arrestors come with the pads, or did you have noise arrestors on the old pads and did not re-install or replace them ?
Did you lubricate the slider pins ? With lubricant specific to the brakes ?
There is something wrong. They should not make noise.
Edit: When you pushed the pistons back, did they go back with just the hyrdaulic resistance, or were they really tight ? A stuck or seized piston can cause problems. Did you inspect all the seals on the pistons and the sliders ? If water gets in, you will have trouble.
If I understand, they are making noise all the time, even when your foot is off the brake pedal. Pay attention and make sure nothing else is touching the rotor or perhaps the wheel rim (just saying). If you are focused on the caliper, it is easy to re-assemble something else wrong that you are not looking at. I can't hear the noise to diagnose, so I have to make presumptions here.
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