How long did it take before Hitler realized the Normandy landing was the real thing?

Well, the Normandy landing was on June 6th 1944

When the allied forces arrived on normandy, Hitler thought it was just a deception tactic

It's not until the end of July before Hitler finally realized it was a real thing.

So, about 2 months

The date of the Normandy landings was 6.6.1944.

This puts the Normandy landings at the beginning of June. Considering the fact that hitler's decrees about a different strategy of defence against the allied soldiers came only toward the end of the next month, it can be said tha it took quite a long; two months, for war time.