The universe may grow very old, and all traces of our wanderings may be lost, but the number 24 will always be 24. No matter what has happened to the means by which a number has been carted about, it remains the same. You then give that paper to someone who paints the number on a sign, and someone who sees the sign enters the number into a computer database. The answer, of course, is that they are all my number. Or, to put it in an engineering context, my number didn't change just because it was being passed around or written in large letters or small figures.
Numbers are inviolate.
And so all you have to do to turn analog sound into digital sound is give each varying volt a number, and maybe a second number, too, to indicate how much it was wiggling. Then you stick the numbers in any convenient storage place - a laser disc is fine, but tape works well, too. Then when you are ready to turn the numbers into sound, you reverse the process. Except for the fact that we need billions of numbers to represent even a few minutes of sound, it's all quite simple. Even people could be used as storage.