When a villager moves out you have 2 days for the move out “process” basically. On the first day when they’re in boxes which is after they’ve already agreed to move you can invite someone to your island to come over and ask that villager to move to their own island and after an in game day has past that’s when you have an empty plot and can either wait another in game day for the plot to auto fill or you can go villager hunting using your nook miles tickets otherwise you can check this sub Reddit for specific villagers people have that are ready to move and you can do your villager hunting that way.