It's a very abstract problem. Because we have only one empirical datapoint. Which is our own existence. You can't prove a negative about the existence of other intelligent civilizations, their time horizons for emergence, yet unknown constraints on interstellar travel, etc.

At the end of the day, Drake's equation sort of bootstraps from

The Law of Big Numbers and then goes from there. So it's a fundamentally statistical argument for which we have no empirical ground for nominator and denominator in the function. Well, we know the nominator is a minimum value of 1, because we exist.