I started asking my LORs in October and gave them all the pertinent information (deadlines, my CV, LOI, and so on) in December. Between December and the application deadline (usually Jan-Feb for public health) I refined my statements and other materials. I started really early thinking I was going to apply for psychology programs as well (due in December) but changed my mind and focused on public health instead. Thankfully, it turned out well.
My only regret was not looking into and applying for scholarships and external funding. Although I plan to apply during my first year, it's unfortunate that I won't have this financial backup this year.