It doesn't matter. He doesn't need to see the future to have a goal and pursue it.
There has been a lot of discussion about what the bounds of Bran's powers are, and very little of it has been conclusively demonstrated in the show. I believe it has been suggested (by D&D commentary? I can't recall the exact reference) that Bran can perceive the future to some degree, though the precision and "fated-ness" of it is unclear.
But he could easily have come all the way to King's Landing to present himself as the best candidate for being king, even if he didn't really want the job, through a mundane analysis of the continent's political situation. That analysis could also have been sharpened by his supernatural grasp of history and knowledge of current events.
He's already said and done things to guide people into proper positions for his plans (or visions of the future, if you prefer) to work (like Arya, the Valyrian steel dagger, and the Night King).
It is not necessary for Bran to have literally viewed these events in advance.
It's also possible that his intentions were even more vague than that: he could have come to King's Landing to help end the wars and deaths that have plagued the world over the course of the show, and upon hearing Tyrion's speech he was convinced that accession was the best way to do that.
It could also be still less planned. Perhaps Bran is simply strengthening the story that Tyrion suggested would make him a king people could rally behind with another dramatic element, for the sake of the gathered council of lords and a future national legend.
The ultimate caveat
The worldbuilding of GoT is extensive, but less emphasized on the show than in the books. Opinions vary on how deep the issue runs, but there are plenty of instances of things not quite adding up on the show (powers described as working one way, but then arbitrarily working a different way seemingly for plot convenience, etc.).
We can always construct baroque explanations for why those things are consistent after all, but they frequently require assertions, varyingly supported by the source material, about how things work more broadly. And neither the show nor the books have purported to explain everything fully, leaving many mysteries where satisfying explanations may hide. This may well be an area in which no true canonical answer actually exists.