For God has bound everyone over to disobedience so that he may have mercy on them all
Is the "everyone" including Adam and Eve before they are created ?
It was always God's plan, before the creation of the world, that all should sin against Him. God is completely outside of time, it makes no sense to speak of things He planned before the creation and things planned after creation. He has an eternal plan, and it has always existed since before the foundation of the world.
Of course, the "all" includes Adam and Eve and everyone else.
The reason given in the verse is so that God's grace can be displayed.
The grace is not given savingly to all, but all receive food and common blessings which they do not deserve.
The plan was God's plan, the blame for the sin is entirely ours.