That's something I've been wondering as well. I've always preferred to have the physical copy, and I'm certainly getting the Premium edition. I'd love to be a part of the Beta as well, but I'm not entirely sure how they'd do that for the physical disc.
From what I understand, if you pre-order a physical copy, you'd either get the beta code on your receipt or get an e-mail with a code. If you pre-order a digital copy, you should be ready for the beta as soon it is available on the platform you've pre-ordered it on.
However, do remember the beta is PS4 and Xbone only. No beta on PC/Steam or Switch.
Contact the place you've pre-ordered from to be sure though.
"Please make sure your retailer is offering the beta before you pre-order the game. If you pre-order a physical copy of Mortal Kombat 11, you will receive a code to gain access to the beta before it begins. The code you receive will be for the same platform that you pre-ordered the game for. Please note, you will be able to redeem your beta code before the beta officially begins, but this will not allow you to download the Mortal Kombat 11 beta until it’s available in March 2019."
I'm so happy that physical editions are getting the beta as well. Can't wait to see what it's all about. I wonder how long it'll last. Didn't the Injustice 2 beta last about a month? I wonder if the MK11 beta would last about that long as well, up until a week or two before the release maybe? Would be dope to have that to satiate our MK thirst for that final stretch.