I have my own theory of the gap, but it's not in Genesis 1:1 and 1:2
Noone ever listens to me when I explain this
In between Genesis 2 and 3 is a gap. Maybe a few years, maybe a few hundred. But in that time, Adam and Eve have daughters and sons. In Genesis 3:20, Adam calls his wife Eve, because she was the mother of all living. But their first child recorded born is not until Genesis 4, after they leave the garden.
So in between Genesis 2 and 3, I propose a gap where Adam and Eve had children, and were obedient to God in replenishing the earth.
What happened to these people? I don't know. When Adam sinned, it says sin came upon all men, so I assume they were cursed as well, or maybe even destroyed, or, perhaps, they were not cursed, and God took them.
There are a lot of holes in this theory obviously. Like, What about the tree of life? Did anyone eat of it? Was it's effects permanent or only temporary.
Food for thought.