Finding possible positions of a polygon within a refined area

In QGIS, I have a geometry (polygon) of a given size and would like to asses all possible placements of this geometry within the refined area. Does anyone have an idea how to do this? If I should be using Python to calculate all possible positions, or if there is another way? Calculation of different geometries must be different to another calculation with a minimum Spacing in X,Y or angle. This can maybe be done by including a list of Y values list of X values and List of angles by defining a area of interest.

Do you know a good method for solving such a problem?

In the picture I show one possible placement of the geometry (yellow) within the refined area (red). The geometry should both be able to be moved, and be rotated.