As soon as is reasonable.
Think of it this way. There are possibly other students competing to work with this advisor, and they might have funds only for one new student. There might be other considerations - maybe the advisor is going on sabbatical, or isn't taking new students, and so on.
So as soon as possible, set up a meeting with the potential advisor, indicate your potential interest (and why!), and ask them point blank if they're taking students, and how they prefer to screen students (some do it through course work, some might like to work with you on an independent study project, and so on).
Depending on what they say, you can take further followup action - maybe they want you to take their class, and maybe they have a research group that has open meetings, and so on.
Bottom line: don't wait till your year is over, because it is quite possible that someone has made a decision already.
Caveat: if this year-delay is institutionalized, it might be that all advisors wait till the end of the year to even think about new students. I suspect this is unlikely, but in any case that first meeting will help clarify it.