Transfer from lower level college to top 50 university, can it be done?

Like lets say you have a kid who did average in High School, graduated with a 3.5 GPA, went to a tier 4 University for the first two years on a full ride. If he maintains a 4.0, is it possible for him to transfer to a top 50 university? Even some Ivies that DO take transfers?

I did it. I got into UCLA.