Depends on how you count.
Vancouver is on the mouth of Fraser River on basically a combination of glacial scouring and sandy infill. The coast immediately adjacent to Vancouver (and indeed, even somewhat inland) is basically your typical fjord system. Thus, Vancouver is surrounded by the west by the Salish Sea, and mountains on all other sides, asides from the sandy coast that stretches south towards Seattle.
Crossing from Vancouver to the Canadian plains requires crossing two main mountain ranges--the Pacific range and the Rocky Mountains. The main river systems here are oriented primarily in a north-south direction, which means they aren't a great help in finding water gaps in the mountains. However, the next major cities to the east in Canada are Edmonton and Calgary, which means any natural highway route is going to want to generally veer north out of Vancouver anyways.
There are basically three crossings of the Continental Divide worth mentioning in lower British Columbia: Highway 16 (the road to Edmonton), Highway 1 (the road to Calgary), and Highway 3 (which hugs the border). In the Pacific Range, these dwindle down to three highways leaving Vancouver itself, Highway 7 and Highway 1 that leave on the north and south banks of the Fraser respectively, and Highway 99 that jumps over to the next fjord north before making its way inland. Somewhat upstream of Vancouver, at Hope, Highway 1 crosses the river and meets up with Highway 7 to continue following the Fraser River due north, while Highway 5 heads vaguely northeast along the Coquihalla, and Highway 3 splits off from Highway 5 shortly thereafter to continue primarily east near the border. Between the two mountain ranges, the connections of roads is rather more complicated, but either way, you're going to filter down to the same bottlenecks when crossing one of the mountains.
And all of those roads I described crossing the Pacific Range? Every single one of them spend substantial portions of its time in a narrow river valley and is currently severed in several places because of washouts. However many roads you want to count it--they are all cut right now.