Yes it is possible to choose the starting month of your calendar if you don't want it to begin on January. This is a bonus for procrastinators who find themselves without a calendar after the start of the year.
Fortunately taking advantage of this feature couldn't be easier. In step 5 of your calendar setup (See below) you'll see that the default start date is the current month. i.e. I wrote this in July, so it is automatically choosing to start my calendar from this month on. If I wanted my calendar to start on a different month/year it's a simple matter of clicking on the pull-down menu for the month and selecting the desired date.