Is it possible to apply to a PhD program, then transfer a year later to a higher-ranked program?
It might be possible, but I would not recommend it unless there are very special circumstances. For example, if your advisor is moving institutions, it might be appropriate to follow them if you have their backing.

The higher ranking program is going to wonder why you were unable to complete your studies at the original institution, and will question your ability to play well with others. They will have many, many applicants that are as qualified or more qualified than you that lack the uncertainties you will bring ("will they stay?" "why did they leave?" "are they being totally honest?"). Further, there is almost nothing you will be able to accomplish in your first year of graduate school that will distinguish you to the point that a school that originally rejected you will suddenly want to drop everything to have you.

Two more pieces of advice: first, the ranking of the school you do your graduate work at matters less than your choice of advisor and ability to thrive in the lab you join.

Second, if you feel like you need more experience or to improve your resume to get into the school you want, you will be much better off getting a research job for a year that is not part of a graduate program - this is very common, and will not be looked upon as strange by an admissions committee. Changing universities after a year will.