It is not due to your drawing skills regarding the slope inclination that I cannot recognize essential details from the drawing: the plane is presumably meant to represent the height of the ground floor floor, but where are the property boundaries? - a second perspective showing the entire property from above could significantly contribute to clarification. Only the development plan can say whether the house fits into the building window.
Basically, there is nothing against having a bay window on the garden or mountain side. But there are several objections to a house requiring a flat plot on a hillside property.
They say faith moves mountains. However, in builders' forums I currently have the impression that hope is supposed to flatten even vineyard plots. But even with outright excesses of earthworks, the magical possibilities are limited.