Construction project and building permit feasible?

Regarding Baukindergeld and building permits.
Assuming you find an interesting plot of land at short notice, you would be free to commission an architect with the design planning and apply for a building permit. This is possible in this country without owning the property.
However, this procedure requires cash, because at this point you will not have a real estate financing. And if the plot does not work out after all, you can at best transfer/adjust the planning for the next plot. A certain loss is inevitable.

Your biggest chance for Baukindergeld is probably an existing property. Forget about "now" and prepare for the future. Clean up your financial situation, settle outstanding debts. Clarify family planning. Save equity capital. Then you will be ready when the right property is at your doorstep. Right now, you definitely are not.
If you live rather rurally, a local network can be extremely helpful. Generally, the leftovers end up in real estate markets on the internet. Most properties do not even get there.

Even a garage costs anywhere from 8 to 40 thousand euros depending on the design and size. And just like a shed, unlike a basement room, these are not heated and things get damp. I’m quoting a post by FrankH, who describes what typical items he needs storage space for:

Suitcases, backpacks, and other bulky bags (if you can still afford a vacation after the construction)
- Strollers and all the larger equipment for children (MaxiCosi, baby bassinets, etc.)
- Vacuum cleaner, mop, bucket, etc.
- Stocks of detergents for all kinds of textiles
- Tools, e.g. all-purpose vacuum, high-pressure cleaner, or small machines in larger quantities (if you are a DIY enthusiast)
- Bicycles, lawnmower, hedge trimmer, scarifier, wheelbarrow, and other garden tools that don’t all fit into the garage (if there is one at all); summer/winter tires (if not stored elsewhere)
- Flower pots/planters not in use, stocks of garden fertilizer, potting soil, etc.
- Computer workstation (getting smaller these days, but e.g. a printer still needs its place)
- Folders (for all kinds of files like invoices, etc.)
- Hobby items (for me, for example, camera equipment with tripod, etc.)
- Pet items if you have or plan to have any (scratching post, litter box, cage, or similar)
- Grill, patio furniture that should be stored in winter
- Seasonal decorations (Christmas ornaments, etc.)
- Books and magazines you want to keep (shelves eventually get full)
- Boxes you want to keep (whether for warranty or resale or as packaging for the next online sale)

Which of these things would you seriously want to store in an unheated, damp garden shed? Bicycles, grill, and flower pots, okay, but otherwise? Inside the SH 142, I don’t see any space for all the other stuff, not even a corner! How large and full is your basement currently? I would want to have at least that much space in total, whether in a storage room, built-in cabinets in the hallway, or elsewhere. Additional areas in the garage or shed are gladly taken as a supplement but are not sufficient as a complete replacement. The technical room of the SH142 is very minimalist; depending on the version of your house, more space must be found there. And we haven’t even talked about the washing machine and dryer yet!

Shift allowance is not (always) included in the bank's calculation because, in theory, it could disappear. 3 rooms in the house must be accessed through a corridor. It has to be longer than for one room with a door. Three rooms with 12 sqm consume more space than 2 rooms with 15 sqm. Technology must be accommodated in the house. Laundry too. Food as well, clothing too. But she did not say at what height. In the end, calculations are done, even at the bank. Words are patient. First, look for a plot of land; that will probably be more difficult than you think.

If we don't find anything for inventory, precisely because of the leftovers, until 2022, building might possibly be back in the running?!