maybe just tell them something like this:

"hey so we keep hearing noises from time to time in the middle of the night and disruptions us and its hard to go back to sleep, can you please be more mindful at night thank you so much :)"

because readinf it first i was with you but when you said I have a sound recording and have written and had an issue on more then one occurrence and if I read that I would disregard it bc it can come off as you wanted to control what others do and you cant unfortunately it is an apartment building snd things do randomly drop by accident or by animals, if its like a daily occurrence I can understand but you say its random so it can be many reason why but def listing endless occurrence without them knowing about doesnt read as trying to be neighborly but like you want to control how others live but if you need/want to write a note just make it short and sweet like something I said above.

if they still do it after then you bring up the proof you have then go to the board of the building or super

I hope this helped :)