Hi,
you're really rushing things....
Short and sweet about your schedule: you can forget it completely. Count on at least 4-6 months of planning and decision time before you sign a contract. Anything less is suicide and will cost you a lot, a lot of money and nerves later on.
Then it takes several months until building applications are prepared and submitted, the building permit is granted, and you have risen high enough on your general contractor's worklist that someone actually starts digging on your construction site. Count on 3 months as a minimum for this step. It can easily take 6 months as well. And then the actual construction time. A solid house will always take at least 6 months, with a basement sometimes 6 weeks more. And that's the minimum if the construction runs perfectly timed. That is currently completely unrealistic. So rather count on 2-3 months more. Weather-related stoppages on the construction site are not even factored in yet.
And that brings us to roughly 13-21 months from today until moving in. I'd guess 16-20 months from now. So somewhere around spring/summer 2021. Twenty-one! So the year after next!!
Prefab houses also aren't really finished much faster. Yes, setting it up on the construction site goes fast, but
a) then you only have a shell standing there. The interior finishing still needs to be done
b) many prefab house companies take more than a year before they even show up on site. By then the solid builder has long since started and has the construction half done.
And on the topic: "we want to have a child"... that's nice, but from personal experience I can urgently advise you to build the house first and then start having children. Building a house can be pretty stressful and exhausting, you don't necessarily have to go through that parallel to a pregnancy. One after the other you can enjoy both, together it can become hell.
Best regards,
Andreas