Basically, I see few problems at first regarding equity and the possibility of getting financing. But I would consider whether it makes sense to go ahead with the house construction now with a high loan-to-value ratio and make substantial prepayments. Then you have today's prices and can fix the interest rates now.
Do it the way Wilder Süden described. Just don't save for too long, credit is your friend! For example, we started planning last year in January, and the first groundbreaking was in October. If you are that disciplined with saving, then nothing can happen to you in my opinion. The problem you will have in the next few years is the construction cost increases, against which you can't save! From 2021 to 2022 alone, it was 10% and more.
To give you a sense of what you get for your money (prices 2021/2022, rural area in southern Bavaria). Our KFW 55 house with a granny flat (total 220 sqm) costs us 650,000 euros. I would say the house is good standard without (major) frills.
Since last week, this house has become 57,500 euros more expensive (thanks to the abolished KfW 55 subsidy). Luckily, we have an approval. KfW 55 will likely become the new standard house, meaning cheaper is not possible.
To fully shock you now: The price does not include a garage, photovoltaic system, battery storage, "smart home" (except automatically controlled electric shutters/raffstores), not a plot of land of course, no landscaping or other incidental costs, and no kitchen either. So in southern Bavaria you end up at about 3,000 euros/sqm if you stick to this standard. Thanks to KfW subsidies, we pay only 2,750 euros/sqm. But that is no longer available.
If you want to make a KfW 55 into a KfW 40+, you need additional insulation, photovoltaic system/storage. I have a quote for a 10kWp photovoltaic system including 10 kWh storage for 25,000 euros. Additional insulation maybe 15,000 euros. Count on 40,000 euros. So the house, if we had KfW40plus, would cost about 700,000 euros.
2021/2022, mind you WITHOUT land and without kitchen.