Some might have an attached liquor store. But they to be in an area that allows that.
Where I used to live, Publix was on one side of the road and could not sell beer on Sundays until 1pm. They built a larger building on the other side of the road and was officially in a different town. They could sell beer and wine all day on Sunday. They also built a liquor store that was attached, but could only be accessed from outside. (This was in Brevard County, btw.)
There also may be an ABC Liquor store on your route, so if you can't find a Publix Liquor store, you may get lucky and find an ABC liquor store nearby.