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.