How to fill mesh shape before extrude?

I know how to fill and extrude a bezier or nurbs shape, but I can’t figure out how to fill a mesh shape made of vertices and edges. Fill commands don’t work (unless I select every two edges to make each triangle). Is there a way or I’d have to remake the shape with bezier?

Alt+F fills a shape

I’ve tried this, but it doesn’t work in my case (the shape isn’t difficult to remake I’m asking to know if I have to avoid making any new shapes this way):

I placed a plane in the scene, then I deleted two vertices so one segment remained. Then I extruded many times making the shape. At the end, I selected the first and last vertices and pressed F to close the shape. Now Alt+F doesn’t work to fill the whole shape at once.