Is it possible to a Villager move out if he/she recently move in? Yes it is, but is a little harder.
1: Do not talk to that Villager.
2: Time Travel day by day 1 week. Talk to someone and let him/her tell you if Muffy or someone else want to move out. If Muffy want to move out TT more until she left, if someone else want to move out look for that Villager and let him/her PING so you can stop him.
Is possible, but is harder. You can introduce yourself to Muffy, but i recommend do not talk to her.
Now, here is an easy way...
-Do you have any Amiibo Cards from your current Villagers. If you have, you can move out that Villager and the recover him/her so the game going to see someone move out and it will be easy to Muffy to leave.
Note: You need at least 10 Villagers to do this.
Hope this help. Any questions feel free to ask, PM or VM me. Good luck!