Can an average family afford a single-family house at all?

Hello dear forum,

I have been a silent reader in this forum for a while now because we (my wife, my child, and I) want to build a single-family house at the beginning of 2017. Thanks to this forum, there have already been lots of changes regarding equipment and basic size. What I have taken away so far are the following points:

[*]Build according to need: 150 - 165 sqm are sufficient for a family of four. Nobody needs the huge 250 sqm houses from the '80s anymore. A plot of 500 to 600 sqm is completely sufficient. More only means work and costs money.
[*]Location, location, location: The location of the new single-family house is very important in terms of value retention and a possible later sale. That means a city or town with suitable infrastructure, shopping opportunities, and development potential is preferable to a larger plot in a rural area.
[*]Look at model house parks soberly: We have already visited many model house parks. And unfortunately, these parks make you crave more. Huge window surfaces, recesses and offsets, open gallery, 200 sqm, conservatory, and so on. What I have read so far in Bauexperte's posts, these are all things that cost huge amounts of money. Therefore, a covered offset, balcony, gable or dormer, basement, and masonry garage have been removed. That means what's left is a simple building form with a timber-frame garage and a small storage room. However, I do not want to completely give up on large window surfaces.
[*]First settle in life, live within the money you have, and then think about financing a single-family house. We have stuck to that. Both are established in our professions and have proven ourselves. Our child is almost 2 years old, and my wife's parental leave and part-time work no longer bring financial surprises. Everyday life with two jobs and childcare works. We drive two paid-off cars and can still go on vacation.

Now to my question:
Is it still possible for a normal family to manage a somewhat "normal" single-family house with 160 sqm, KFW 70, air-to-water heat pump, and ventilation system with heat recovery?
Summary:
Single-family house in monolithic construction (brick or solid wood wall).
2 full floors
Gable roof
KFW 70
No basement
160 sqm
Air-to-water heat pump with ventilation system
Large window surfaces on the ground floor (of course not continuous, but a bit more than a simple balcony door is acceptable... I hope you know what I mean).
Normal window surfaces on the upper floor
500 - 600 sqm plot (no slope)
Timber-frame garage (with storage room)
Covered terrace
Two 15 sqm large children's rooms and a small guest / office room are planned.
Electrical work is done by my best friend (master electrician). We get materials for our own equity.
More electrical work besides possibly painting is unfortunately not feasible or sensible (if you are not top-skilled handy and do not want the construction phase to turn into a divorce phase).

The plot is located in Upper Bavaria (on the border to Lower Bavaria and thankfully far enough away from Munich. Prices from Munich increasingly push into the outskirts). The sqm price is between 230 and 250 euros (fully developed, price is not finally fixed yet).

And now to our financial situation:
I (civil servant / 32) earn 3365 euros (without Christmas bonus etc.).
My wife (employee / 32) 1435 in part-time (26h per week), without bonuses etc.
4800 family income
We have no ongoing loans.

We have equity of at worst 100,0000 and at best 150,000.
Our warm rent currently amounts to 800 euros.
I can currently save at least 1000 euros per month (it can also be more sometimes, depending on what expenses our daughter produces).

Apart from the high equity, I find our income situation quite average (if you partly consider the wages and salaries of other building families in the forum).

Now to my question. Can we manage it or are we taking on too much? I don’t need a palace to show off. I also don’t want my single-family house to dominate me and invest every free minute and cent into the new single-family house. Purely on instinct, I think it would be doable. But the rising costs, as well as some construction cost threads with insanely expensive excavation costs etc., honestly scare me quite a bit.