X user Ben Crew poses an interesting question.
My immediate thought was John Kennedy because of how he handled the Cuban Missile Crisis, which I think might be similar to first contact with aliens. It was necessary for Kennedy to be firm and project strength to deter the USSR and thereby avoid a nuclear war, but also restrain the hotheads within his administration who wished to invade Cuba and instigate a nuclear war. Kennedy's brinksmanship could be optimal for showing strength until the nature of the aliens could be determined.
For somewhat similar reasons, I'd also suggest Abraham Lincoln. His political coalition was profoundly fragile and fragmented. He had to keep to his goal to subdue the rebellion while not leading to a split within his side that could have led to a Southern victory. Lincoln knew how to listen to his advisors while not being enthralled by them.
Yes, Lincoln predated what we could call science fiction and thus would not have a mental map for alien life, but that itself could be useful because science fiction norms might lead us astray in the event of actual first contact.
Of course, Crew's question assumes that a President or even Presidents have not already experienced first contact with aliens.
-via Aelfred the Great
Previously on Neatorama: In a Mass Knife Fight to the Death Between Every American President, Who Would Win and Why?