According to Orthodox Judaism, has God always until now desired that every person from Israel and other nations to repent from their wickedness with a broken and crushed heart(Psalm 51:19) and be saved, no matter how sinful he or she might be?

It’s written in Kohelet (7, 20), “For there is no righteous man upon earth that does only good and doesn’t sin (literally: mistake)”. And just as everyone sometimes wrongs, everyone can and should fix that wrong. R. Simcha Bunim of Pshischa writes that God doesn’t punish man for wrongdoing, for He made us in a way that it’s inevitable. He just punishes one who doesn’t utilize the capability to “return” and right that wrong, for anyone can change directions and improve. But I must add that as any loving Father, in addition to the necessary humility and awe in the verse you cited, there also needs to be the love of our Father and His Torah, and most important sincere regret and a future change of actions. Remember God is Perfect and doesn’t need anything, but wants our goodness and improvement for our sake.