Is building a house on a low budget still possible with the current prices?

Ground floor: Hallway, kitchen (possibly with pantry), living room, utility room, guest bathroom, guest room
Upper floor: Bedroom (possibly with dressing room), 2 x children's rooms, bathroom, small storage room
- Outdoor facilities: Terrace, double garage, cistern

I am a big fan of guest rooms; I find a guest room on the "valuable" ground floor at least unusual. Is working from home even an issue for you as a mechanical engineer? What I can really recommend then is a study room from which you can directly see the street; that is the perfect starting position for receiving package deliveries :)

What I really appreciate right now with kids is a large hallway/vestibule, a spacious eat-in kitchen, and a sufficiently large pantry.

A dressing room can also easily be separated off with a wardrobe. We did that to keep the use of space more flexible.

we want to fulfill the dream of owning our own home, but we have major concerns about whether it is even feasible with our budget and income. Maybe you have experience and can give us tips.

Specifically for your individual case, I will refrain from commenting; there are experts for that. In general, as a technical construction advisor, I can tell you that especially in the area of "it might work, but only on a modest scale," unnecessary hesitation (mostly due to the unfounded hope for a miraculous price drop soon) would not be advisable.

Whether solid construction, prefabricated house in solid or timber construction is initially not important. We are completely open on that.

The prefabricated solid ICON houses from Dennert Massivhaus also sound interesting.

Being open to different construction methods is already very good. Some providers offer attractive stages of the partial-finish house concept, also for limited self-builders. I don't think badly of the Dennert Massivhaus Icons, but to me they appear to be one of the most rigid offers on the market.

With your budget, you can easily build (have built) a single-family house for the 4-person family anywhere in Germany. Your "problem" is your wishes. Two years ago, this would not have been a problem at all, since loans were practically free. That's why there is whining everywhere today that no one can afford a house anymore (I don't mean you). Build only the house you need - 150 sqm, double garage, upscale fittings, finished outdoor facilities, pantry, etc. are "luxury." But really necessary? No.
Cleverly planned 125 sqm provide three bedrooms + office. Instead of a garage, a carport. Garden tools etc. go into the garden shed. And so on.
Add a few DIY efforts and you can easily build a house for the family.

I know the place from you and can gladly recommend something to you.

Please keep us updated.

I have almost exactly the same starting situation.

We could cover the plot from equity and have a maximum of €450,000 available for the house. (Girlfriend currently on parental leave & 1-2 more children planned)

Only, I don't have an electrician at hand but two master carpenters.

Regards

We pay most of it to the carpentry for our wooden house, so you're already in a good position with two master carpenters ;)