Well, the series never really went in certain directions that were easily justifiable. Even a small tribe of humans taken from here two or three thousand years ago, given somewhat modern medical care (antibiotics), improved farming methods and crops, and other 20th century niceties, would have a staggeringly high population by now. Starting with just 50 people 3,000 years ago and maintaining a 1% growth rate would give you a potential population of about a quadrillion people, enough to populate a million planets with a billion people each.
By our standards, 3,000 years is a long time!
*** boring math part ***
At this same growth rate (only a tiny bit more than the current US growth rate) the population would take 300 years to increase twenty-fold, so the fifty people would've become a thousand. So 300 years for the first good sized village, 600 years for the first small town, 900 years for the first medium city, 1,200 years for a medium sized state, 1,500 years for a good sized country (150 million), 1,800 years for a planet of 3 billion, 2,100 years for 20 such planets, 2,400 years for 400 such planets, 2700 years for 8,000 such planets, and finally 160,000 such planets. If you assume a 2% growth rate (still moderately low by third-world standards) you get 100 million planets with populations rivaling Earth's, and all from just 50 people snatched up 3,000 years ago.
The writers probably weren't spending too much time with a quick population growth spreadsheet.
A quick lecture about that in the briefing room could launch a set of story arcs, with vast numbers of humans off in some other galaxy, which they've filled up like tribbles.