In order to understand what is meant by God giving dominion of the earth to Man, you first have to understand what the earth was like before God created Man.
The earth before Man was 100% Naturalistic. What do I mean by that? Everything behaved in accordance with natural laws. If I drop a penny, the only path it can take is down. It can do no other. Well, the whole earth and everything on it was like the penny. Everything event on the Earth happened because it could do no other, the laws of nature forbid it from doing anything else.
God has complete dominion over his creation at this point. If God wanted to add an oak tree to his creation at a certain time on a certain field, he could. Furthermore, he put the tree there in such a way as to preserve the continuity of his creation. If God simply popped a tree into existence, that would represent a discontinuity. One moment in history the tree was there where it wasn’t the previous moment. This would not be naturalistic. The sudden existence of the oak tree does not follow by natural laws.
God exists outside of our time. Instead of “magically” making the tree appear, he could send a squirrel to bury an acorn in the right spot. And, of course, instead of making the squirrel “magically” appear, he could give the squirrel parents to raise him. Since the entire Earth is Naturalistic, God could extend this process back to the beginning of time. Each event causing the next event until the oak tree grows exactly where God wanted it to. This preserves creation’s continuity. Anyone inspecting the history of Earth could find no evidence that the oak tree grew where it did for anything but natural reasons, even though the tree was deliberately put in exactly that location by God himself. The universe was created in such a way that from the very beginning, the growth of that oak was inevitable.
Now if God creates human beings with freewill all this changes. God cannot micromanage the universe in the same way. Humans have freewill. What is the guarantee that some farmer would not choose to plow the field under to plant wheat? By creating freewill human beings, God is willfully suspending his own dominion over his creation. God cannot put trees where he wants to anymore, at least while still preserving the naturalistic continuity. God of course could still choose to pop the tree into existence wherever he pleases.
God really did give people dominion over the earth. If a person wants an oak tree in whatever field, that person can put it there.
