I agree with Mikey and Shilo.
I almost stay away from this subject because there are literally a gazillion opinions on how to break in a barrel. Even the premium barrel manufactureres and gunsmiths vary quite a bit. Some folks do some hand lapping, use JB bore paste, etc. to hasten the polishing process while others use a variety of shoot/clean/shoot/clean cycles, and everything in between. Good results are reported with a lot of different methods. I'm not a bench rest shooter and honestly, I don't hold my expectations to tiny fractions of an inch because I am primarily a hunter and a casual shooter - but I do believe in good maintenance and taking care of my guns. I think it makes sense to break in a new barrel with some care, and I agree - a bore snake is not the right thing to start with.
I will have to admit to having used both methods - some judicious use of JB and/either/or Flitz - or the shoot/clean/shoot/clean cycles. I don't think I've screwed anything up too badly - my guns all shoot better than me, but like I said, I don't have the expectations or requirements that others might have.
Bottom line to me is - it is worth some extra care to break in a new barrel and keep it clean, use the proper tools, and be careful of your crown when you clean.