Don't whistle before you are out of the woods proverb
Don't conclude a problem solved until it is completely resolved.
"Your heart operation was successful. You are no longer in any danger" - "There might be some complications. Don't whistle before you are out of the woods".
"The problem will be solved if he agrees to help us." - "Don't whistle before you are out of the woods".
If you take a flyer (on something), you take a chance, risk, or gamble on it.
The coach took a flyer on the young goalkeeper, and it turned out to be a wise choice.