ᐅ Placement of the Gutter / Rain Gutter

Hello dear experts/builders,

I have a big problem with where to place the gutter on the south side of our new build.

On the left side of the house, there is a corner window on the ground floor, so from my point of view, proper rainwater drainage is not possible.
What does it look like if a pipe goes past the corner window?

On the right side, there is a ground floor extension with a flat roof—see the attached photo.
According to the construction company, drainage is not possible here!
But surely there must be a way, right?
Could someone please help me with this?

An internal drainage system is also difficult. We are building with a timber frame construction method.

Thank you very much,
Veronika1979

Why can’t a downpipe be installed directly at the left edge of the house (which is in the middle of your photo)? The extension is located next to, not in front of, the house, right?

So, the extension is the area with the wooden cladding, located right in front of the house… The part with the door is the back of the recessed garage

Ah, do you have a floor plan of the relevant corner of the house?

You can also drain in the middle or offset from the middle, depending on what works best or looks better.
One picture alone doesn’t give me much to go on.

In the center, I actually didn’t want an ugly drainpipe ☹
And I’m having a bit of trouble sharing complete house elevations and floor plans publicly… We really paid a lot of money for the plans.
Maybe the section shown here is useful?
I would prefer to drain either around the corner on the east side or through the extension….