PulseAudio has a module to suspend audio sinks (outputs) after a few seconds when devices are idle
Try removing the module temporarily first:
pacmd unload-module module-suspend-on-idle
If that works to eliminate the noise use this command to comment out the module load command in PulseAudio configuration:
sudo sed -i '/load-module module-suspend-on-idle/s/^/#/' /etc/pulse/default.pa