Financing a detached house of 140m2 in Bavaria - Is it possible?

Hello everyone,
I would like to make my dream of owning a home come true and hope that some experts or experienced people here can give me their assessment.
My current status:

[*]The plot (800m²) has already been purchased and will soon be fully paid off. The value is probably currently around 105€/m², so presumably about 84,000€.
It is also fully developed.
[*]This plot is my equity.
[*]In addition, I have a financial buffer of 20,000€.
[*]After consulting with a construction company, the shell is expected to cost around 160,000€ (a written offer will arrive soon).
[*]My bank has promised me financing of 350,000€.
[*]Total budget therefore about 450,000€.
[*]Desired size 140m2 living space, possibly also a garage with usable space in the attic and a door to the upper floor to create storage space and further options for later.
I no longer expect to have a basement due to cost reasons.

Now to my question: Is this budget enough to build a single-family house? I am aware that besides the shell, many other costs will arise (interior finishing, electrical, heating, sanitary, outdoor facilities, etc.). I have already started a cost calculation but still do not have all the offers.
Does anyone have similar experiences or can estimate whether my budget is sufficient for a solid single-family home with standard features? Where could unexpected cost traps lie?
Is anyone perhaps here who has recently realized something similar?
I look forward to your opinions and advice!
Thanks in advance!

Maybe a few additional details:
A lot of the work should be done by parents, friends, and acquaintances. However, the "professional tasks" must be done by companies.
My expectations are not very high; for example, the garage can be paved, so the concrete slab could be omitted there accordingly.
Features like a fireplace, etc., are not necessary either; I am planning a heat pump.

A prefabricated house might also be an option; some advise against it, others say it’s great.
Maybe you can also share your experiences here with a similar project? Does it make a big difference in price? How is the durability?

If at all, it is only possible with the cheapest providers offering prefabricated floor plans combined with a lot of own effort, but even then I see the budget as extremely tight.

Normally, you calculate with €3000/m² (in Bavaria rather €3500). Just with that, you would be at €420,000. However, the budget without land is only €370,000. And the house itself is by far not everything. There are still additional building costs, landscaping, garage, kitchen, or even a photovoltaic system (I believe mandatory in Bavaria since this year).

Therefore, I would normally estimate the total project for the house without land at around 550-600k.

Realizing the whole thing with 370k is therefore very ambitious.

The best thing is to browse through all the threads here, then you will get a good feeling for the total prices, individual cost points, saving potentials, etc.

You must not include the 20k buffer. You need it for the necessary purchases upon moving in.

Leave out the garage.
What about the outdoor area?

Ask at Town & Country what a standard house costs in your region. Around here you don't hear anything bad. They are budget-oriented houses. If it is around 300k it works.

First read, then write. Usually, in this forum, one can read 5 times within 10 minutes how expensive a house per sqm is nowadays in Germany. And due to the north-south gradient, a calculated average value of 3000€/sqm results, whereby it should be said that Bavaria is the most expensive, ultimately many things are regional. For all your other questions, this thread is not sufficient - however, all your questions can be found numerous times here as answers if you read a bit in the forum.

Does anyone have similar experiences or can estimate whether my budget is sufficient for a solid single-family house with usual standards?

Normally without EL: about 450k for the house, maybe 30-50k additional construction costs, 30k for the garage, x for driveway, garden, terrace & co. Now you have to estimate what you can cover through family & friends. It will be at least exhausting and time-consuming