If it is good for you, you can start ANY time.
I dislike the concept of "New Years Day." It's a pain in the neck: I have to remember to change the Month AND the Year when I write a check (not I write many checks, but you get the idea), the mortgage is still due, the credit cards still need to be paid, and the gym is full of people who won't be there in 31 days.
And we often see questions from runners: How can I train for a marathon if I can't do my long run on Sunday? Saturday is better for me. What shall I do? ... Duh, run on Saturday or as I do Friday. There is nothing sacred about long runs on Sunday.
So, start your new lifestyle on Friday, or Wednesday, or St Swithins Day.
Just get started!
Start by doing what is necessary, then do what is possible and suddenly you will be doing the impossible -- St Francis of Assisi
Rock 'n' Roll Dublin Half Marathon, Dublin, Ireland, 8/5/2013 ie.competitor.com/dublin/