How do you prove that without walking into a post hoc ergo propter hoc scenario.
I would hold it to be self evident (as I explain one paragraph down.)
But if you consider it for a minute it is a performative contradiction to suggest that cognition proceeds from emotion, rather than visa versa. That would mean that some emotion randomly, stochastically, arrives in your brain, and causes you to initiate a cognitive process about something. In this case emotions are the dictates of the universe and there is no ability to change the mind of another, because there is no way to get at the cause of the thought; Humans become television sets pointed at eachother. So, in arguing this point you invalidate it. Because argument presupposes a mind to change, and that cognition is the root of the other person's position.
But one does not need the above argument as it (cognition preceding emotion) is self evident. Emotions always presuppose a
something at which the emotion is aimed, even if the
something is yourself or the universe. Emotions tied to nothing are literally unthinkable (and I challenge you to try come up with one.) Further, emotions always proceed cognition in your experience; You feel terror when you
understand (i.e. gain cognizance of) some terrible event. Events you never learn of you have no emotional response for.
NB: The above is not to be confused with music which is a special not-well-understood case.