I haven't experienced any white noise but doing really heavy exercise an hour before sleeping tires my body out and makes it easier to sleep , it can also help to do a breathing technique where you breathe in completely and as much as you can while tightening up your entire body and then relaxing it completely , doing this 10 times as I fall asleep works well for me.

If you are feeling agitated because your mind is filled with a lot of non random thoughts ( emphasis on non random thoughts like arguments , rants and a constant stream of opinions , random whacky nonsensical and abstract thoughts are good and indicate that sleep is about to come ) , its best to wake up for a while and do something to distract yourself . like when I find my mind full of arguments and can't sleep because of it I just wake up and play chess on my phone and then go to sleep a bit later when I am tired and ,mentally relaxed .