Your mesh is a mess however,i doubt it would work.If you want to create a face manually you can select 3 vertices or more and press the ‘f’ key,it’s best if you try and keep your mesh all quads though (you have some Ngons in there which are bad news)
The method you describe (pressing F to create a new face) is exactly the same as what I said I’ve been doing, the problem is that it just ignores the vertices in the middle and creates a square. I want the new face to just ‘fill in’ the blank bits.
Despite blender having n-gons which tend to create at least one face in most impossible situations you are better off ‘normalizing’ what they are allowed to do.
For the figure you show there are two ways:
separate ‘cloudy’ geometry and use it as a knife cutter later, after you create one face there.
connect some of the ‘clouds’ vertices with corner vertices of the square with edges and fill faces consequently; n-gon can’t ‘live’ inside other geometry and be not tied to it - it needs at least two edges which connect it.