My first villager, Sprocket asked to leave in week two of his own accord, I didn't have to do anything to get him to leave. I didn't have to be mean or ignore him so that was really fortunate! My other starter would take like 6 months of ignoring to get them to leave. It was torture and I felt really bad! I did use an amiibo to move out my random campsite villager as well. Sometimes villagers are quick to want to leave, other times you may have to wait a long time or use an amiibo to get rid of them for good!
Best way outside of time travel to get someone to leave your island is to wait until someone has a thought bubble about moving away.
If someone asks to move, turn the game off without answering them. They will still have the thought bubble the rest of the day.
But the next day the game picks again what villager will be asking to move out. (It could be the same villager again)
Repeat that process until the villager you want to leave asks to move.
It could take a long time, but at least there is no waiting period between villagers asking like when you tell them to stay. If you do that it's something like 2 weeks before someone else will ask.
Or if you have the amiibo of someone you want, you could kick them off within 3 days. This is my preferred method as I have access to every amiibo XD
Your starters will ask to leave like any other villager. They may be comparatively less likely to leave over newer arrivals since you would talk to them a lot and do jobs for them and build up friendship with them for several days before the game lets you move villagers in and out of your own will. Given the time, though, they will ask permission to leave, yes.
All of my starters asked to leave relatively quick i feel like. I also used amiibos cards as well. I kept my two starters because i loved both of them and was so excited to see that they came to my island so i kept them for a long time and still have one. The three that came after that all moved out pretty quick i feel. I didn’t use any trick or anything on two of them and then i moved the last starter with an amiibo card.
I tried ignoring a couple villagers that I had and fencing them in and it took longer to get them to leave than it did for the ones I actually talked to and befriended.