100% and you probably know this, so I'm just addin: think of infinity as a sequence of infinite numbers. The number of all the even numbers, that stretch off into infinity, are also infinite. However, that infinite number isn't as big as regular infinity.

You can have different sizes of infinity because when things get that big, the rules change. Its almost like infinity / 2 = smaller infinity.

Well, they wouldn't write it instantly - in the best case, they would start writing it instantly, and finish in optimal time. However, it's possible that no monkey would actually write it on the first try - we'd have to get into some complex predictions on monkey brains and physiology, it's possible that with their brains and muscle structure they wouldn't go for the kinds of character sequences to produce Hamlet, perhaps changing up patterns enough to produce something more random only after a certain amount of time.

Depending on how you formulate the experiment, it could be that no monkey could finish it before physiologically having to take a break or something, returning to specific patterns afterwards that would render it impossible for it to finish writing Hamlet, and thus no monkey would ever write Hamlet in a continuous string of characters, from start to end.

But yeah, if we just say they're typing completely random characters without pause forever, yup, infinity dictates some fraction of monkeys would immediately be on the right track and finish writing as soon as possible, for anything you can think of.