Blogging is not a piece of the Professional Writing resume. Blogging is a personal decision and something you should do because you really want to, not because you think you need to. Blogging is time consuming and sometimes difficult, but it can also be very rewarding and a lot of fun if it's something you're actually passionate about.
It seems like your question is more like - should you blog if you've decided to persue writing as a career and the answer is, no. You don't have to blog to build toward writing as a career. You should only blog if it is something you really love doing.
And in that respect, you can start any time!
Spend plenty of time thinking about what sort of blog you want to run, what your content will be centered around, what sort of people you want as your audience. This will help you build your blog. Decide how often you want to blog and make a list of topics that covers 4 months. You don't have to use them all and you can change your mind along the way, but if you can't think of enough topics to fill in once, twice, three times, or five times a week for 4 months, you're going to have some trouble updating your blog reglarly. Then start researching the different platforms and services. They come in all shapes and sizes. Most are free, some are not. Figure out what you can afford right now and what you want to afford in the future.
Make a list of all the blogs you love to read and seem to be pretty successful. Figure out why they are successful and what you love about them. Put that information to good use for yourself.
Once you start your blog, if you can keep up a regular schedule of posts and you keep improving your content, you can expect to start gaining followers around the 6 month mark. It takes a lot of leg work on your part to find followers and bring them to your blog and lots of time and effort into giving great content. But it'll happen if it's something you really want.