April 24, 2020
I'll start with the bad news (which is pretty bad). Last year, Yale accepted about 2% of its transfer applicants ... a number that's markedly smaller than the puny 6% acceptance rate for freshmen. Candidates who are admitted as transfers to Yale commonly come from atypical situations. They are often non-traditional students (i.e., older) or hail from disadvantaged, underrepresented-minority backgrounds. In other words, they are students who probably wouldn't have applied to Yale at all straight from high school.
You don't say if you're a recruited athlete or a student of color, so I'm guessing that the answers to those questions are no and no. Thus, the fact that you have already had the opportunity to attend a snazzy private school will probably push you to the back of the transfer-admission line without some special “hook." You could bust your butt to earn straight A's for a year at your initial college, and it's unlikely to help your acceptance odds at Yale. If you work just as hard in your second year, your chances will not improve unless, perhaps, you can point to a really head-turning accomplishment during that time ... e.g., you publish a novel, you write a symphony that's performed at Carnegie Hall, or you pioneer a medical breakthrough ... curing cancer or, at least, baldness. ;-)
The good news, however, is that if you manage to maintain that 4.0 GPA (or close to it) throughout your college years, you may position yourself well for a second shot at Yale, via graduate school. The graduate acceptance rates are about as daunting as the undergrad ones are, but admission committees this time around will be most focused on your specific academic achievements in your field and won't care so much about who was president of the class, who played tuba in the marching band, or who can shoot 50% from the 3-point line.
The other good news is that, even if Yale is your “dream school" as a teenager, by the time you are 21 and have been successful at another institution, you may discover changing priorities and goals. As poet Robert Frost once said, “ ... way leads on to way." So the college choice you make next spring could eventually point you in a different direction, far from New Haven.
However, if Yale is indeed your dream, 'The Dean" does not want to discourage from applying this fall. I don't know enough about you to insist that you have no prayer. And even if you are certain, yourself, that your chances are minuscule, this may just been an itch you have to scratch before you can move on.