Speakers have noise with new head unit

I installed a JVC KW-V20BT head unit in my 2006 Acura TL. The car has a factory amplifier that does not use RCA and I hooked the remote turn on for it to the head unit, as well as all the speaker and power wires.

The first time I turned the head unit on, I do not remember hearing any noise, and I played a song with it fine. There may have been noise, but I can't accurately remember. I then powered it down and secured the wires. I powered it back up again and I now notice noise playing through all the speakers with 0 volume and no music playing. When I turn the volume all the way up the noise gets a bit louder.

I tried plugging in/unplugging the antenna, and there are no RCA cables going into the head unit. I wiggled the wires around a bit to see if maybe a wire was picking up some noise from a power wire. The noise only starts once the head unit fully turns on. There is still noise with the car's engine off.

Could this be because the speaker wires from the head unit are already amplified by the head unit and then sent to the factory amplifier? Could I wire the speaker wires, the ones that go to the factory amplifier, to RCA plugs and plug them into the RCAs on the head unit to get rid of the noise?