Could I choose to allow a copied spell resolve before original spell with Primal WellspringApproach of the Second Sun must be cast from the hand to win the game on as a second cast; however, the first one does not have to be cast from the hand. So, could I cast Approach of the Second Sun for the first time in the game, use a white mana from a transformed Primal Amulet Flip to copy the hand casted Approach of the Second Sun; but, choose to allow the copy to resolve first and therefore win the game?
Primal Wellspring copies the spell when you cast it. The copy will always resolve before the original. However the copy is also not cast, it is simply created on the stack, and will therefore not satisfy the "...and you've cast another spell named..." clause. If something allows you to cast a copy it will specifically say the word "cast". Some examples of this are Mizzix's Mastery or Isochron Scepter.