[svachalek]

Actually, the article explicitly calls out that step as one potential "great filter". It also (click the link) lists the theoretical ways it could be accomplished.

It seems to leave out the Von Neumann Probe:

https://en.wikipedia.org/wiki/Self-replicating_spacecraft

This is not exactly colonization but possibly an easier step. Either way, the point is that if either we or our machines can get to another star system and repeat the process from there, exponential growth means it pretty much doesn't even matter how long it takes. In astronomical time, we'd cover the galaxy in the blink of an eye.