How long would it take for an independent group of space settlers to take over a planet?

I see a lot of media describing large space colonies, and am curious as to how they got there. I'll admit, I'm mostly inspired by Interstellar here. So here's the scenario:

A group of 600 settlers, hand picked for genetic diversity and equipped with the latest technologies, land on a Goldilocks planet similar to Earth. Trouble is, Earth has fallen to a catastrophe and they are the only humans left, so they're on their own. Thankfully:

• They are all young and strong, and none of them are suffering from any genetic conditions that may shorten their life (they are the last hope for humanity after all)
• In their ranks are skilled scientists, charismatic leaders, brilliant engineers, and generally outstanding people who can contribute to the colonization effort.
• They have the equipment needed to analyze their new home, avoid most dangers, and figure out their food, water, and shelter.
• They have means to generate renewable energy
• They have enough knowledge between them, and written down, to recreate almost all earthen technologies
• Their ship is outfitted with some technologies that help in mining, farming, metallurgy, and automation, but new ones definitely need to be built to expand the colony. They also have effective ways to locate natural resources.
• There are no indigenous species smart enough to be competition for them.

The technology they posses is post-modern, but not super futuristic, mostly faster, quicker, more efficient versions of things we already possess. With these ideal conditions, how long would it take for the colony to start building cities? to take over the planet? or do they just not have a chance?

EDIT to make things simple, the planet is considered taken over when at least 25% of habitable land is inhabited (the planet is earth-like in size and geography), there are at least 3 cities on par with Manhattan in size (but not population, no need for so many high rises), and technology is at least the same level as what they started with. I'm not a master at population dynamics but 500 million seems like a good number of people to have in total.

posted over 7 years ago

Jim Wu‭

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