Without a real sill and a slope on the outside your going to have water intrusion. Add a gutter/diverter above the door on the roof. Remove all the sealer you can. Use waterproof concrete sealer/paint on the slab. Fill every gap you can with silicone. Shave down the slab with an angle grinder to add some kind of slope.
If the concrete applier ‘forgot’ to add a slope to the outside see if they will help with the remedy.