Yes. Of course, if by "nontraditional credit or alternative credit" you mean something other than getting a standard mortgage.
There's owner financing. Then there are things like lease-options, lease-purchases, contract for deed, and so on. There's a technique called "Subject To" in which the owner deeds the property to you but the mortgage remains in his name. There's equity sharing and co-signing, where you're relying on someone else's good credit in order to purchase.
And that barely scratches the surface.