Hearthpwn

I've always found the beginning of the season to be the easiest time to rank up for me personally.
I think it's because when the season rotates, a lot of people just start playing meme decks and less high tiered ones (possibly because they fool themselves into believing the climb will be higher later in the season? Who knows?).

From about the middle of the month onwards the panic begins to set in for players who haven't reached the next ledge yet and they then start to play more aggressive decks and look for ways to rank up quick before they run out of time.
I imagine this part of the season is easiest for those playing counter-meta decks since they will start seeing their prey a lot more often and will rank up. 

Finally at the end of the season you get the hard core players who have messed around all season and now just need to rank up before the end of the month hits. This is most definitely the toughest time to rank up because the majority of players will be trying to do it here. 

So if you want an easy ride up the ladder, get it done in the first couple of days, I would say.