I believe your actual problem right now is that your current apartment is too small. Of course, you want to offer something to a child, but at toddler age, it doesn’t necessarily need its own bedroom yet. If that’s absolutely not an option for you, I would first solve the problem and start looking for a suitable rental apartment. That might not sound as fancy as buying, but it will solve your current problem for now.
Then I would deal with the topic of building and, as already said, downsize the house! Really calculate how many square meters each room actually needs. We are building 140 sqm with two small children, without a basement, garage, or anything else, and have a higher monthly income than you. Lower your demands, otherwise this really won’t work at the moment!