Human overpopulation
Since God knows the future, He knew Adam and Eve would sin. This explains why He already had a plan in place to redeem fallen man. The first prophecy of Christ comes in Genesis 3:15 , which states that He will come as the seed of a woman/virgin birth (see also Isaiah 7:14). If you look closely at Genesis 2:17, God foreknew that mankind would sin: “for in the day you eat of it.” He didn’t say “if you eat of it.”
Theoretically, let’s say that that sin did not happen—no original sin happened, the human population exploded, and people filled the earth. Pay close attention to what God said: fill the earth, not overpopulate it.1 The command was to populate until the earth was full, and then reproduction would cease. Similar statements govern sea creatures (Genesis 1:22).
Consider if someone asked me to fill up a glass of water for them. Would I fill it and then keep putting water in it so that let it overflowed? No, I would fill it only until it was full. The word fill basically places limits on humans right from the start. Nonetheless, if sin never entered the world, then there is no reason to assume God wouldn’t have said “stop reproducing” once humans had filled the earth. Remember in a world without sin, God’s relationship with mankind wouldn’t be tarnished; hence, open communication should still be there.
God can and does change some civil rules from time to time. For example, originally we could only be vegetarian (Genesis 1:29), but after the Flood, God gave man permission to eat meat (Genesis 9:3 ). Also, there used to be rigorous sacrificial laws, but now they are done away with due to Christ’s perfect sacrifice. But such changes happen in our sin-cursed world.
After the Flood, Genesis 9:1 and Genesis 9:8 reaffirm that man was to reproduce and multiply and fill the earth as well. The basis for overpopulation comes from uniformitarianism and projecting current growth rates into the future. Uniformitarianism has failed in the fields of geology and radiometric dating while looking at the past. So, why trust the results of uniformitarianism here?
We can be sure that God knew humanity would sin. To deny this would be to deny that God knows the future, even though He declared that He tells the end from the beginning ( Isaiah 46:10).
Animal Overpopulation
From Genesis 1:22 and Genesis 1:28 , we can infer that man and sea creatures may have had lower initial populations so that there would be plenty of room to multiply. With humans, there were only two people to start with: Adam and Eve.
Birds were to multiply but not commanded to fill the earth, so it seems they may never have filled the earth before their reproduction would have ceased in a perfect world. But they must have had room to multiply too. Regardless, sin entered into the world, so such “what if” questions are mere speculation.
Land animals were not commanded to multiply or fill the earth in Genesis 1 . I would suggest that this implies land animals were created in more abundance—with little or no necessity to reproduce in great quantities in a perfect creation. 2 After sin, though, this became a necessity, since death began reigning in animals. The first recorded death of an animal was the one used to cover Adam and the Woman’s sin (coats of skins in Genesis 3:21).
Later in the Bible, we find that land animals on the Ark were told to multiply abundantly after the Flood, which had caused a massive worldwide graveyard of previous animals (Genesis 8:17). Since there were no land-dwelling air-breathing animals (Genesis 7:22 ) on the earth after the Flood (except for those in the Ark), this makes sense—their populations were low for this new starting point. These land animals were not told to fill the earth, but at this point they lived in a sin-cursed world were death reigns, so an upper limit may have been unnecessary.
So no, the curse would have been irrelevant to overpopulation in a perfect world. We need to remember why there is a curse (i.e., because of sin).