The Germans aint getting a bomb that early without massive changes to their nuclear program, such as one massive centralised project similar to Manhattan instead of several small, poorly funded groups. They would also need to find funding for it somewhere at the expense of the rest of the war effort, I've heard that by removing the Aggregate rocket program they could have covered the costs but even with that they're still removing funding from armaments. They'd also need to all their research in a place both removed from the threat of Allied bombing and the Soviet advance, something which was becoming harder and harder by 1944.
Even if all those factors use ASB magic to allow the Germans to have a bomb in the double figure kiloton range by D-Day there are still issues, the Germans don't have a plane which could drop the bomb, and even if they did the Allies would have total supremacy of the skies, making such an operation too risky. They could simply put it in a bunker on the beach and wait, but they would most likely have it in Calais, where they thought the invasion was going to come. As such they would probably have to wait until the Allies had advanced to use it.
Using it to try and hold back Operation Bagration would have made much more sense, strategically and just pragmatically.