The moment the alarm goes off is the first test; it sets the tone for the rest of the day. The test is not a complex one: when the alarm goes off, do you get up out of bed, or do you lie there in comfort and fall back to sleep? If you have the discipline to get out of bed, you win - you pass the test.
Since the team understands that the leader is de facto in charge, in that respect, a leader has nothing to prove. But in another respect, a leader has everything to prove: Every member of the team must develop the trust and confidence that their leader will exercise good judgment, remain calm, and make the right decisions when it matters most.