Faith in operation...not inoculation.

There is a serious difficulty with the Calvinist notion that “saving faith” is injected into the elect (and maliciously dangled in front of the reprobate) to bring about salvation.   Where does this idea leave Adam?  If God injected Adam with saving faith (wasn’t he, of all persons, predestined "before the foundation of the world?") in an innocent constitution, then how did it not work as well as that injection given to depraved Paul?  Does it need the cross to make it active?  If so, why all the humbug hubbub about “before the foundation of the world?”  If not, then how could Adam lose his gracious condition and predestine the rest of us with him to sin. (I Corinthians 15:47-48)  If God did not equip Adam with “saving faith,”  then how could he ever be saved; or is he?