So what was it like to you? You're kicking around on a serene autumn day that's just beginning to settle into night, and the scream of a hawk patrolling above does what to you? Is it unsettling? Alarming? Exciting? Ominous?
You may not need to say "out of nowhere, we heard the scream of a hawk." You could convey the serene atmosphere, say what needs saying about it, then start a new paragraph:
But the sharp scream of a hawk patrolling above broke through the silence and reminded us that all was not well.
Or:
When we heard the sharp scream of a hawk patrolling overhead, both of us were alight with excitement. "It's back!" we yelled together.
Hope that helps. I like your description of the autumn day.
ltd.