Sooner or later we all run into an impossible situation. A lose-lose, where it looks like we get the raw end of the deal whatever we do.
But God isn’t threatened by our impossible situations. He is bigger than the seemingly hopeless, and can establish ways through.
Sometimes he even seems to create insurmountable situations (Gideon in the Bible comes to mind here, among others) so we learn that He can overcome them. And so we learn to rely on Him and not so much ourselves.
Jesus constantly dealt with insincere religious leaders (who felt threatened by Him) who attempted to put him in lose-lose situations. Examples include the woman caught in adultery in John 8:1-11, paying taxes (Matt 22:21), etc). He always had a solution.
Ephesians 3:20 (which you’ll see references to throughout this site) promises that we have a God “who is able, through his mighty power at work within us, to accomplish infinitely more than we might ask or think.”
Sometimes God gives an amazing solution to a seemingly unsolvable problem. Sometimes He gives wisdom and courage. Sometimes he says “wait”. But he always has the best solution.