If you have the audio do what Meytal Cohen does, use a digital audio workstation (DAW) to place your audio there, then select the first say.. 30 seconds and place it on a loop, play along to it until you cannot make mistakes, then go back to the DAW, add another 30 seconds to your original selection, play along until you make no mistakes, add the remainder in 30 second increments until you have now the entire piece, play the entire piece from beginning to end and you should be able to nail ANY drum piece this way.. You can slow down parts that you don't understand in order to hear what is going on and of course looping will create repetition which will embed the song in your memory, committing movements to muscle memory is not that hard either. Don't overthink it.
A quicker way is to listen to the song, write down the main parts and play using that, for example:
Intro: play pattern 8 times then singing starts.
1st verse: pattern 3 times
chorus: (chorus pattern [if different] 2 times)
2nd verse: pattern 4 times
And so on...
I never done either one of those, I just listen to music in my car on my way to work and on my way back, roughly a 350 song playlist on a thumb drive.
Never have played most of those songs, but I could because I got the parts committed to memory.
A lot of my YouTube videos I have never before played the song ( I have heard it many times but never played it) I pressed record and winged it hence a few mistakes here and there but they were one take videos with no prior practice like this one:
