God desired that Adam not fall---but He did nothing to prevent it. The Bible says that God desires for all men to be saved and come to knowledge of the truth.
Some of the "OSAS" people believe in "predestined-election"---which holds that God
wills for some to be saved, and these He irresistably "helkuo-drags-draws" to Himself, the rest He leaves in their sins, to perish. Purporting that the perishing is their own fault, nevertheless denying that it is GOD who holds the responsibility (the "elect" would also have perished, because of their "total depravity", but only because of God's intervention---thus, those who perish most certainly DO have an excuse---it may be their SINS that condemn them, but it was God CHOOSING Hell for them by not DRAGGING THEM FROM it as He did the
also-perishing-ones-which-became-saved)...
Our ("OSNAS") belief is that God has a will (Jesus was purposed to die on the Cross, God's WILL from the foundation), but we believe that the application is that He
allows them to receive Christ or reject Him. In this belief, Jesus died for all men---it is absolutely possible for every man woman and child who ever has/is/will live can be saved. And this would please God immensely. But, His sovereignty allowed Him the application for someone to
choose to love Him, or to choose to reject Him. What God wills, happens---what God desires, He gives leave to happen or not.
God's nature is absolute good, and ultimate perfect. He is also ultimate just---and I do not believe "just" includes deciding who will be rescued from Hell, and who will be left alone to perish---those who perish, for justness to exist, must do so on entirely their own choice...
(I also do not believe God has "several wills"---thus I read Rom12:2 as ONE will, which is good AND acceptable AND perfect; there are those who read this as
three different wills)
We all seem to agree on what "gets us saved"---it is receiving Jesus as our Lord and Savior. We disagree on things like, "where does
faith-to-salvation/belief come from", we differ on "salvation being FELLOWSHIP/ABIDING-IN-HIM". I persist in debates because I believe the answers to these questions shape our very walks, and in reality our very eternal destinies.
If salvation is "God-willed and God-maintained", it is a very different walk than if "God allows us to endure/persevere IN HIM, or NOT"...
BTW, to say "Nothing happens outside of His will", may be true, but to say that He is responsible for the evils in the world is false. Obviously He allows a certain lattitude in worldly affairs. I only say that there is also a lattitude in our (the "elect") walk with Him...