We have the technology.Hmm ! I have just thought of a problem with sending frozen eggs into space. I was thinking test tube baby's are grown in a test tube. But actually when the egg is fertilized the egg is planted into a female womb to grow.
To grow eggs to baby's without a womb would require technology we probably don't have, and may never be able to create.
Researchers Have Successfully Grown Premature Lambs in an Artificial Womb
Wow ! So my idea of sending frozen eggs into space is a possibility. All we need now is robots that are intelligent enough to rear them. This means we could send ships to the stars, even if it took hundreds of years to get to a habitable planet. There are other issues, like what psychological effects children being brought up by robots without human adults, would suffer from. But the possibility of colonising space by this method exists.