I think we're in agreement save for semantics.
I don't think people have an opportunity to be saved because God determines it 100% of the time. Since we can't change God's decree of the future I don't see there being an "opportunity" as I define the word.
I would say we are without excuse because God says so and not because man has the ability to independently do "A" or not "A". To illustrate, I can show God is unjust from a human stand point. Consider:
Premise 1: John 3:18
but the one who does not believe [and has decided to reject Him as personal Savior and Lord] is judged already [that one has been convicted and sentenced], because he has not believed and trusted in the name of the [One and] only begotten Son of God .... people who never heard of Christ go to hell (not talking about age of accountability ... let's keep it simple)
Premise 2: Billions are dead that never heard of Christ (keep it simple so talking about after Christ died)
Conclusion: God is not just because He has requirements for humans that they cannot achieve... now GOD is just so it must be true, but from a human standpoint the above does not seem just. Same idea with the word EXCUSE (giggle ... looks for lightning bolt to hit ... I'll probably get balled out like Job)
Similarly.... I think we have no choice when it comes to being given a 'sin nature'. It's not my pick, I was born with with evil desires (Romans 7:18). Being created with with an evil disposition seems like an good excuse from a human point of view ... Looks for lightning bolt again.
In the final analysis God is the potter and we are the clay and if He makes one vessel to be adopted as His son and another vessel to go to hell then that is justice even though neither vessel determined its fate (hard determinism). We are 'responsible' because a higher authority (the potter) says we are responsible and not because we are capable of obeying.
God is not partial to anyone (Job 37:7-8;
2 Timothy 1:9; 1 John 4:19; Romans 9:11; Acts 10:34; Romans 11:34-35); He determines all things, everything goes His way. God accomplishes His purpose and not ours. We have no intrinsic worth. We work as designed; there is no other First Cause.
If God's knowledge of his creatures were derived from the creatures by the impression of anything upon him [as Free WIllyism or compatibilism suggests], he could not know from eternity, because from eternity there was no other source of information but himself; and therefore what is eternally known by God must be initiated by God. Stephen Charnock and some of my editing