Would it be possible to reconstitute a biosphere from scratch using seeds and eggs? That would be a thorough test of what we actually know about the ecosystems. What do we need from the earth, air and water? What viruses and microbes are needed? And how could the ecosystems be rebooted? There is a lot of interdependency. You may not be able to reintroduce some type of life without the ecosystem created by previous generations of that same life. The behaviour of animals is formed by their parents and the environment. It would be a very complex puzzle to recreate all the things humans would need. A Human child needs a lot of microbes for the gut and skin.
But there also is a lot of resilience and adaptability. The earth has undergone radical changes during millions of years. Some forms of life survive others die out. But we want to create and nurture the ecosystems needed for the prospering of human life and that would include most of the nature we lived with for the last 10.000 years.
The terraforming system in Horizon was named GAIA, constructed to act independently until a new generation of humans was ready to take over responsibility. It was constructed to care about the continuation of all life and that love guides it decision making for situation where it would be logical to make harsher actions, or no actions at all. It's programmed to hope for the best. It has nine subordinate functions named mostly from greek gods, here listed in the approximate order of activation.
MINERVA (goddess of wisdom) has the job to break the codes to shut down the initial machine plague that destroyed all life on earth, build antennas to send out the deactivation code, and then signal the start of the terraforming process.
HEPHAESTUS (god of metalworking) has the job to build factories that produce all the terraforming machines needed. It starts out with the systems to build acquisition machines that will gather materials for expanding the construction. It has codified knowledge of general engineering in a way that lets GAIA imagine new machines for every situation and iterate on the designs for continual improvement.
AETHER (the blue sky) has the job of detoxifying the atmosphere. It would regulate the gases composition to make it suitable for the reintroduction of life. Particulates could be added or removed to regulate surface temperature and weather patterns. Flying Stormbird machines would take part in measuring the atmosphere and process it with electrical charges.
POSEIDON (god of the sea) has the job of detoxifying the waters. It would filter the waters, giving it suitable composition with pH, minerals, oxygen, et al. Larger machines will filter the water in the sea and smaller ones like Snapmaws does the same for lakes.
DEMETER (goddess of agriculture) has the job of reintroduce vegetation. It would clean the earth recreate the topsoil properties for suitability of life. It would probably do this by introducing the right mixture of fungi, bacteria and other microbes, along with suitable flora from cryogenically preserved seed stocks. Several machines are used for the conditioning of the topsoil and planting of seeds.
ARTEMIS (goddess of animals) has the job of reintroduce fauna. It would start with invertebrates (like insects) and other smaller life forms required by larger animals like fishes and rodents. The first generation would have to be grown in an artificial environment mimicking the womb and parenting, with nutrients and microorganisms. The animals would have to be reintroduced in the right order, using stopgap solutions for replacing the functioning of other animals before they had time to establish. Many machines would be used to monitor the developing ecosystem and rein in species that risks dominating other developing life.
ELEUTHIA (goddess of childbirth) has the job of birthing and raising human children. It places cryogenically preserved embryos in artificial wombs, giving them the right nutrients and environment. Androids nurture the children, teaching them a language and preparing them for school.
APOLLO (god of culture) has the job of giving all the knowledge to the new first generation of humans. They will use gamified education with virtual reality interface to teach and train the children to understand, survive and prosper in the new world.
HADES (king of the underworld) will work as a reset function. It's a safeguard that will restart the terraforming process if it finds itself in a unrecoverable state. Developing a computer system will usually involve hundreds or thousands of restarts while trying to get everything right. The complex and chaotic nature of biological ecosystems makes it likely that one or more restarts will be necessary.