The first crack at (something) noun phrase
The first opportunity to do something
Have you ever tried bungee jumping? - No, I haven't. This is my first crack at it.
You have been waiting for 2 years to have the first crack at confessing your love to her, but why did you give up so easily?
She gave the Director the first crack at reading her script, but he denied.
I will take the first crack at the mission.
Nothing but fortunate chance
If you take a flyer (on something), you take a chance, risk, or gamble on it.
The last opportunity for one to achieve something
A second opportunity
Very little chance of succeeding in doing something
"First crack at" is believed to first occur at least as far as 1841. By 1848, this phrase was already being used metaphorically.