Question: does anyone know when exactly Cullen got transferred to Kirkwall? If I'm not mistaken, he's already Knight Captain at Act 1 no? And when did Samson got kicked out from Templar Order? If I'm not mistaken Cullen & Samson shared room together for a time. Am I right?
I'm having another idea for another fanfic (none got finished...) about this... Zero romance/love story type of fanfic anyway 
Cullen is still in Ferelden at the time of the Battle of Denerim, which is more less six months after Hawke arrives in Kirkwall. Hawke only meets him once their year in servitude is up, though, so if we assume Cullen was immediately transferred to Kirkwall after the archdemon was defeated, and place the first time Hawke meets him immediately at the beginning of Act 1, that gives Cullen about six-eight months in Kirkwall before they first meet Hawke. You can make it even longer by pushing the start of Hawke's involvement with the Order to very late in Act 1.
He did get promoted to Knight-Captain soon after he got to Kirkwall, yes. One possible scenario (what I'm using in my own fic anyway) is that Cullen and Samson roomed together in the first few months he was in Kirkwall, up until Samson was kicked out, and soon after Cullen got his promotion. Another is that Cullen might even have already been promoted by the time Samson left, he just didn't have his own room yet because the acommodations in the Gallows were precarious and there wasn't enough room for individual quarters until the one he shared with Samson was vacated one less bed. We don't know much about that either way, so it's all up to interpretation.