How do I get this thing to appear after I created the mesh
You can’t. This panel is called Adjust Last Operation, and it disappears after you do next thing.
You can only bring it back for a very limited time. If, for example, you have just clicked away from it because you thought you were done, and then you go “Oh no! I wanted that cylinder to only have 8 vertices!”, you can do Edit → Adjust Last Operation or press F9 to bring it back. But only for as long as you haven’t done any other operation – even if you just go into Edit Mode and then leave without having done anything there, you can’t bring it back.