In my view, God had three choices after the Fall:

1. Save no one. This would have exalted His holiness, and been perfectly just.

 2. Save everyone without restriction. This would have compromised His holiness and mocked His justice.

 3. Save some by means of an atonement effected by a perfect Substitute of His own choosing according to His own will for His own glory. This would not only exalt His mercy, grace, and love, but also His wisdom, righteousness, and all else He is. To His glory, it would enable Him to be both just in His dealings with rebellious, unregenerate mankind, as well as the justifier of everyone He chose to adopt as sons out of unregenerate mankind by means of this gracious atonement and His sovereign work of regeneration.

(cf. Mt. 20:28; Isa. 53:10-12 with Rom. 3:24-26; 5:14-21; 9:16, 18; 11:5)

 Most, however, would offer some form of a 4th option:

 4. Save all who produce “acceptable” good works. But this would make salvation impossible, for God Himself has declared that "There is none who does good, there is not even one" (cf. Mark 10:26-27; Psalm 14:1-3 with Romans 3:10-12).

God “owes” salvation to no one. Therefore, He must save graciously or no one will be saved. And God must save sovereignly because not only will unregenerate man never seek Him, but ANY work, including a work of self-generated faith, would provide a basis for boasting to the one who produced the work. Hence, according to Scripture alone, salvation is granted by sovereign grace alone, and effected through gifted faith alone in Jesus Christ and His perfect and finished cross work alone so that all glory redounds to God alone.

For by grace you have been saved through faith; and that not of yourselves,

it is the gift of God; not as a result of works, so that no one may boast.

For we are His workmanship, created in Christ Jesus for good works

which God prepared beforehand so that we would walk in them.

(Eph. 2:8-10; cf. 1 Cor. 1:30-31)

Amen and amen.