Do that sort of stunt as much as you like, it won't become something more. It's like trying to jump over a building by hopping a bunch. You can hop one time or one billion times, you won't clear the building because after each failed hop you're back to square one.
Such a small group of people, armed with current genetic engineering and future artificial means of reproduction, could bring with them enough genetic diversity and reproductive capacity to reach colonizing scale.
You can hop one time or one billion times, you won't clear the building because after each failed hop you're back to square one.
Despite the first part of my reply, this point about minimum activation energy is relevant to a lot of contexts, from escaping poverty to switching careers, from getting fit to overcoming medical conditions. This is a pretty good analogy that I might use in the future.
The hard part I think is "playing factorio IRL" on a planet we weren't evolved to cope with. Bootstrapping industry sufficient even to create additional shelters would be very challenging. Maybe we could practice this on Mars.
I don't mean this as a personal attack, but that gets the idea dangerously close to the theory of unfalsifiability.
Personally I am more inclined to the believe that we haven't heard any radio signals from space because you don't run a multi-galaxy civilisation on light-limited transmissions.
Invent the ansible and then maybe we will find the galaxy theming with life.
That's ok. Insignificant numbers are more than enough to colonize an entire galaxy on geologic timescales.
The thing about the "Great Filter" is that it is great. If you can even imagine an exception for your candidate filter, then it's not great enough.