There's still say a billion year window. The jurassic was 200 million years ago. If some spacefaring civilization developed at that time on some other planet, and the galaxy could be colonized in a few million years, they could have done it a hundred times over since the dinosaurs.

The distances in the milky way are mind boggling. But the age of the Earth is even more so.

As an aside: The technology / evolutionary differences are likely to be immense. Imagine trying to have a 'first contact' with an ant in your backyard. Honestly, for most humans, it's not even close to worth the time or energy to 'talk' with something like that. We don't even consider a single ant worth of much study at all.

Now imagine a people as far advanced of us, as that ant is to you. Now imagine that 10,000 times more advanced. Or 100 million times more. That is the kind of difference we have to consider.

The unfortunate reality may be that other civilizations are so far advanced from us (100x? 10,000x? 10 billion?) that we are effectively 'alone' all the same. Like an ant pondering the garden hoses, BBQs, or fence posts of the universe.

I think that calculation only works if you replace "colonized" with "explored". Automated, self-replicating probes could reach every star system in the galaxy by moving and spreading as fast as they can but effectively colonizing each system would take a lot longer. This isn't a game of Civilization where you just pump out settlers, real colonists need a reason to leave everything behind and stellar scale civilizations probably take thousands of years to mature and fully exploit their star system. I think the article is closer to the truth.

If colonizing a star system to be able to send further expeditions would take 500 years, and an interstellar trip took 500 years, there's still a thousand "colony generations" in a million years.

Call me pessimistic (I'm not) but I think it would take longer than 500 years to achieve a large enough population level to fully colonize the space around a star. You could assume that our current trend of declining population would reverse and we'd begin breeding like rabbits once we start living in space habitats but I don't think that's very likely. I think there's a good chance it would take us thousands of years to fully saturate a star system. We'd have to master living in space as well as building generational world ships/habitats that could traverse interstellar space on multi-generational journeys. Personally, I think the most likely state of affairs (if you assume a hard boundary of the speed of light) is that civilizations colonize a small group of local stars and then begin in-filling the space between them once they know how to build fully self sufficient habitats. This is similar to how we currently exploit the most resource rich areas on our planet and then develop out along transportation networks when we need more space. Outer space is three dimensional though so this process likely takes a much, much longer time. All that assumes no major breakthroughs that allow FTL or radical different modes of being though.

Exponential growth can do quite a lot in 500 years. What happened to North America?

During that time, the population of Europe increased as well - many people just thought that America was a better place to live.

There's no need to wait for "full saturation of a star system" to send out probes and colony ships.

The population of North America is around 579 million after 500 years of exponential growth and probably the largest and longest sustained immigration trend in the worlds history with only open ocean as a barrier. We're talking about a star system with potentially multiple planets and moons let alone interplanetary space to colonize and century long gulfs of empty space to cross. My money is on it taking longer than 500 years before any native born son of a new star thinks to theirself that they could make a better life even further out.

I made the point in another comment but I do think there has to be a reason to send out colony ships. I agree that exploratory, unmanned probes would be sent out to gather information but I doubt sustained efforts to colonize new star systems would be made until there was significant social, political, or environmental pressure to do so. One ship colonies never succeed beyond a toe hold, you need a constant flow of people, resources and information to drive the founding of a new civilization especially if the trip is one way with little possibility of trade. If all you needed for the development of a new culture and society was an initial seed population and time then every town in the world should be a New York.