re: It's just stupid how big space is and how small Earth is

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1. The Sun is a typical star, and relatively young. There are billions of stars in the galaxy that are billions of years older.

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Sol is not a typical star. Red Dwarf stars vastly out-number any other star type.

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2. Almost surely, some of these stars will have Earth-like planets.

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Earth-sized exoplanets are not the best candidates for life, in fact. "Super-earths," which are 2-3 times the mass of our world are much more plentiful and are more likely to have water and other necessary chemicals for life than do earth size exoplanets.

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3. Assuming the Earth is typical, some of these planets may develop intelligent life.

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Our only example casts doubt upon that proposal. Single-cell life originated on earth 3.8 billion years ago. However, it took 3 billion years for multicellular life to appear. Sentient lifeforms, us, appeared about 200,000 years ago. By our example, intelligent life is much more unlikely than simpler lifeforms.

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4. Some of these civilizations may develop interstellar travel, a technology Earth is investigating even now (such as the 100 Year Starship).

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In my opinion, we cannot traverse space in our present forms. We must either become cyborgs or create A.I. to travel away from our solar system.

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5. Even at the slow pace of currently envisioned interstellar travel, the galaxy can be completely colonized in a few tens of millions of years.

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Maybe, but I don't think colonize is the right word. It's just too big even for exploration without some new physics.