In season 11 we have seen that every time the Darkness eats a soul it grows a little bit stronger. At the end of season 10 Death tells Dean that the Darkness is older than God and more powerful, as he says that God and his archangels could not destroy the Darkness but only lock it away. So why does the Darkness need to eat souls to grow stronger? If it is older than God then there would not have been any souls around for it to eat at that time and yet it was still more powerful than God, so why does it need to eat them now?
The Darkness was Reborn. She had no physical form yet on this new planet God created after her imprisonment. She possessed a baby perhaps to give her time to learn more about this world before getting her revenge. After being trapped for that long it'd be foolish to attack God blindly. The souls seem to help her grow. Think of her vessel as a bottle and her power as a stream of water flowing into the bottle. The bottle grows as her vessel matures. She can harness more of her potential power. She's also probably pretty rusty having been sealed for so long.
Not necessarily stronger
I don't know that it is accurate to say that she is stronger than God. She is different. She is the Darkness. She eats (absorbs) energy. So you can't incinerate her or produce energy to destroy her. That will just make her stronger. Of course, she said that she was stronger than God, but she wasn't necessarily truthful. Further, even if she thinks of herself as stronger than God, she isn't necessarily correct. Perhaps God thinks the same, in reverse.
Perhaps you might say that she is a stronger absorber than God. In theory, someone could absorb energy from her faster than she could absorb energy from someone else. But God either couldn't (or wouldn't) do that.
During her long imprisonment, she had no one from whom to absorb energy. So she grew weaker and weaker. When released, she could not produce much energy, but she could still absorb energy. It's unclear if God could have overwhelmed her then. Perhaps she didn't know. Perhaps she lacked the energy to produce godly intelligence. As she grew, she absorbed energy faster and faster. Could she always have maintained that rate? We don't know.
Maybe God didn't want to
She's God's sister. Maybe it wasn't that God couldn't kill her (whatever he may have said) but that he didn't want to.
We can't really say one way or the other, because the Supernatural God is not always truthful. Perhaps if he had tried to destroy her, she would have just grown faster. Perhaps he loved her too much to destroy her and was willing to allow the rest of his creation to be destroyed instead. Perhaps it would have been a bad idea.
It's possible that attempting to destroy the Darkness would have damaged her in ways that were not helpful. Perhaps destroying her memories and her connection to God, so she would have lost what little restraint that she had. So we could have been left with the ravening hunger and no sentience behind it.
In a similar vein, the Supernatural Wikia says:
Mandatory Existence - Amara's existence is necessary and provides balance to reality. As God put it, "Light needs Dark", and "Dark needs Light". If she were to be killed, reality itself would end. However, it was said that if both God and the Darkness were to die, a new balance would be established.
Again, killing the Darkness isn't necessarily impossible, but it still might be a bad idea.