In Genesis 1:28, after God made Adam and Eve, He told them to "Be fruitful and multiply and fill the earth and subdue it, and have dominion over the fish of the sea and over the birds of the heavens and over every living thing that moves on the earth." At that time, Adam and Eve were both physically perfect and spiritually pure. Neither they nor their descendants (had they had any) were cursed with death. So wouldn't the human population have quickly reached a number that was unsustainable for the earth's resources?
Why did God tell Adam and Eve to fill the earth—if no one died, wouldn't the earth have become overpopulated?
There are two misconceptions that lead to this line of thought—one major and one minor. The minor issue is that the earth was untainted by sin, as well. We don't know what the earth looked like before the Flood, but we can say a few things. There was no pollution. Most likely, there was less landmass covered by water, fewer (if any) deserts, and the mountains were shorter. And before the Fall, there were no weeds. In addition, as stewards of the earth, these hypothetical perfect people would not have damaged the land like we have. The earth could have supported a much larger population than what we see now.
This is the minor consideration because even with a perfect earth, eventually there would be too many people.
The second misconception is the show-stopper. If God put Adam and Eve on the earth with the mission to care for it and all the plants and animals, why would He then forget about the potential for overpopulation? How could the Creator of the universe Who had carefully aligned dozens of very specific universal constants into perfect harmony create a being that, by its very God-given nature, would destroy that creation?
He wouldn't. But He wouldn't necessarily tell us His plan to prevent global catastrophe, either. Perhaps He would have made the human race stop having babies. Or maybe He would have taken people as they were ready, and given them glorified bodies on a new earth. We really don't know, and the Bible doesn't say. But we do know that God would not have created a "very good" (Genesis 1:31) world and forgotten one little thing that would have destroyed it.
What is the tree of the knowledge of good and evil?
Why are such long lives recorded in Genesis?
How old is the Earth?
Was the Noahic flood global?
Did God create the universe?
Truth about Creation