it probably makes more sense to argue that the byzantine empire is the continuation of rome, but in a broader sense, all of human civilization is the continuation of the indus valley civilization
The point being there isn’t a single cause to the fall of Rome and there are even a few arguments that Rome continued in various forms, some of which still exist today.
There are several reasons we could argue that the Roman Catholic Church is the continuation of Rome and so Rome never truly fell.
That is what I was trying to say in the previous comment.