On a wing and a prayer
Definition 1 of 2
Pro Tip 1/3Optimistic Undertone
Implies hopefulness despite acknowledging risks or difficulties. 
He started his business on a wing and a prayer, believing in his vision.
Pro Tip 2/3Facing Challenges
Often used when someone faces obstacles but still pushes forward. 
She started the race with an injury, running on a wing and a prayer.
Pro Tip 3/3Less Formal
Suitable for casual conversations rather than formal writing or speeches. 
I'm just gonna wing it with the repairs and hope for the best.