A few schools do offer rolling admissions, meaning that candidates are admitted as applications come in till the class is full.
However, the bulk of acceptances are sent out in the earlier rounds. Schools tend to use the last round to fill the remaining few spots in the class. Competition for the last round is extremely fierce. Since the number of available spots is very low, the number of applicants per spot is high. Furthermore, schools might have waitlisted or reserved judgement on many candidates in the previous rounds. All of them are included in the assessment in the final round.
Hence, we strongly recommend that you apply in the early rounds. Moreover, many schools encourage international students to apply in earlier rounds to allow for sufficient visa-processing time.
The ideal time to start gathering information about schools and developing your story is about 5 months before the first round deadline of your target school. This would give you time to research the schools and craft an interesting application package.