The soonest it would happen is the 2030s. I follow the NBA. There are currently 30 teams. Most around the Association believe that the next two franchises will be Seattle and Las Vegas, and afterwards the NBA will restructure from being 2 conferences of 15 teams to 4 conferences of 8 teams.
Vancouver could get in on the next expected expansion of 4 teams that'd stretch the league from 32 to 36. Mexico City might be in the running as well.
Upcoming TV deals are likely to influence Vancouver's odds of getting an NBA franchise. Currently, the largest TV deals are domestic US deals, like TNT, ESPN and NBC, and in these cases, Canadian viewers effectively don't count. More international and online TV deals for the league as a whole would probably increase the odds of more non-US teams in the NBA, like one in Vancouver.
Another factor is that Raptors owners, rogers and bell, are used to having basically no other competition in the Canadian telecomm and sports broadcast markets. I think that they would have the means and motivation to effectively block another NBA team from expanding into Canada.
Well if it's any consolation, the results of this post (at time of writing) are currently pretty close to the results of the poll. Although our sample size leaves something to be desired.
The question needs to be asked that if British Columbia's are so in favor of an NBA franchise, why didn't they support the Grizzlies when they had them?
I'm personally ambivalent on this topic but I did consider this question and it seems that the popularity of basketball has grown quite a bit since the Grizzlies moved. That's an old article but if anything is probably more true today than when it was written.