TNG started with the entire crew needing pregnancy tests, including Data.
However you want to explain the stuffiness in the pilot, no one was getting over that impromptu orgy in The Naked Now until the command staff had recycled 95 percent of the rest of the crew off ship.
Of course a repeat of all that mating lust in Genesis just meant that they had to start their three card Monty shuffle with quarterly crew evaluations all over again.