I have created a mesh object using the extrude 'tool' as follows using default CUBE (which has the default material removed), merged at center (press M select merge at center) and then extruded along x and Y axis to create a multi-sided 'plane' which I then extrude on the Z axis to created 'thickness'. I then FILL the top and bottom 'faces' by selecting each edge in edit mode and then press F. When I add a material if I select just a color all faces are 'painted' with that color HOWEVER if I select Image texture it will not uv wrap. Am I using an incorrect method to fill?
Make sure your faces are properly marked as inside/outside.
You can do this by going to Viewport Overlays > Face Orientation, and recalculate it by going to Edit Mode > Mesh > Normals > Recalculate Inside/Outside. Also, make sure you apply any transformations using CtrlA.
Alternatively, I achieved the same result as you by extruding along the Z axis AFTER pressing F to fill the face, which seem to play nicer with blender's UV wrapping.
P.S: Why are you using this roundabout way to create and extrude a face? If you're not specifically attached to the process, you can achieve the same result by scaling the default cube along the Z axis, or using the Solidify modifier on a plane.