No you don't have to wait because as soon as you order the physical copy, you immediately get a code on the receipt that allows you Early Access to Stormblood.
I believe the OP is having that small worry that I had when I ordered my physical copy from Amazon. After I pre-ordered my game, I got a code along with instructions on to how to enter the early access code to the PSN. I entered and it said 'code redeemed'. I went to Mogstation and sure enough Stormblood EA is listed under my account, but there's no circle on the PS4 box. To be absolutely certain that the code made it through, I went to Playstation Network website and checked on my recent purchases; sure enough, the Stormblood EA was listed.
I believe once the material is available and is automatically downloaded into the platform, maybe by THEN the Mogstation will confirm that you have early access on your PS4.