According to this article, mankind is nearing its 33rd doubling.
If you divide The 1,656 years from the creation to the flood by 33, you get 50 years per doubling. That means that if the pre-flood world population doubled twice per century, and no die-off due to famine, war or disease occurred, then the population would equal our current population. This permits allowing for them to get married later and start having children later than us, as seems likely from the genealogies in Genesis.
It took 39 years to go from 3 To 6 billion in recent times. See https://en.wikipedia.org/wiki/World_population_milestones
Thus the limiting factors would be Disease (much less prevalent, as evidenced by longer lifespans), technology (lower than today), arable land (the flood devastated the earth and messed with the climate, so probably more arable land in their day), and warfare. The last is mentioned in the Bible. Thus I would put the population as less than today, but not by too much: perhaps 2.5. Billion people.