I don't think there is a finite number of monkeys that would be guaranteed to do so in the lifespan of the universe.

Best we could do is calculate the expected number of monkeys it would take, assuming accurate probabilities, which I also don't think is possible to determine.

You can't just take one divided by the number of possible characters that could be typed because monkeys can do many things other than typing away. A high portion of them would likely instead destroy the typewriter. In the infinite monkeys scenario, an infinite amount would destroy their typewriter in the middle of Hamlet's to be or not to be soliloquy.

Plus the odds of it actually happening are going to be so astronomically low that if you filled the known universe with monkeys, you'd end up with monkey stars and black holes before any Shakespeare.

It really only works as a thought experiment about the nature of infinity.

Unless there's an infinite multiverse, in which case we are in the universe where a monkey wrote out the complete works of Shakespeare. That monkey's name? Shakespeare. (And yes, many clapped when he did so.)