I was thinking of the cheapest most effective way of colonizing space quickly and I find that once cryogenics are mastered all we have to do is send a small crew of women with thousands of frozen embryos at their disposal.

After taking off on AI controled ships that keep them in stasis for hundreds of years with a recyclable supply of oxygen and food those founding mothers land on habitable worlds build up settlements and start populating them with the genetic diverse stock of embryos.

Keep the first three generations female only and a crew of ten could spawn a thousand humans assuming each female has ten children from age 20 to 40.

After the third generation males should be introduced in the population as half of the fourth generation and normal breeding should be allowed between people three times removed.

With a settlement reaching 10.000 people in under a hundred years an effort should be put to rebuild and refit the colony ships for their voyage to the next habitable planet.

Assuming we travel at one hundred of the speed of light using future technology in 5000 years we could colonize the nearest star systems (50 ly away) and in 12 million years we would have all of the Milky Way.

Food should be mostly lab grown as grain and meat tissue can be kept in cryo during travel but need hydroponic kits stored in ship for early settlement building.

Other key equipment should be 3D fabricators, mining kits, metalurgy kits and a contained habitat for 20 people should the planet turn out to be inadequate for breathing and radiation exposure.

Additional equipment may include a small cache of firearms should hostile fauna be encountered.

Do you think this idea could work? Do you have any additional tech and suggestions that could help space colonization in this way?