Rules Analysis
A thrower who is lying down or kneeling does not need to establish a pivot.
A thrower lying on the ground will have several points that could be their pivot, but they do not have to declare which point is their pivot, unless they choose to. If they subsequently decide to stand up, they can choose which point was their pivot, and establish their foot as their pivot at that point.
If they stand up it is not a travel, provided the pivot is established at the same location.