Well, please re-read John 3:16 very slowly. It is not an offer, it is a statement of fact. Later in John, you will find that no one can come to Jesus unless He draws them personally.
The gift of God is eternal life in Christ Jesus. God draws us lovingly. He does not “drag us kicking and screaming”. Otherwise it would be coercion. God is not Allah. He is too dignified not to give his subjects a choice.