Jn 3:16 does not say:
"Grace makes salvation available to all men."
Yet the Scripture does say...
Tit 2:11 For the grace of God that bringeth salvation hath appeared to all men,
Tit 2:12 Teaching us that, denying ungodliness and worldly lusts, we should live soberly, righteously, and godly, in this present world;
As well as...
2Pe 3:9 The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance.
2Pe 3:10 But the day of the Lord will come as a thief in the night; in the which the heavens shall pass away with a great noise, and the elements shall melt with fervent heat, the earth also and the works that are therein shall be burned up.
2Pe 3:11 Seeing then that all these things shall be dissolved, what manner of persons ought ye to be in all holy conversation and godliness,
Those two passages clearly teach that God does not want ANY to perish. Repentance (2Pet 3:9) is surely the means by which one yields to grace teaching of godliness (Tit 2:12, 2Pet 3:11).
John 3:16 is within this context...
Joh 3:16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
Joh 3:17 For God sent not his Son into the world to condemn the world; but that the world through him might be saved.
Joh 3:18 He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God.
Joh 3:19 And this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil.
Joh 3:20 For every one that doeth evil hateth the light, neither cometh to the light, lest his deeds should be reproved.
Joh 3:21 But he that doeth truth cometh to the light, that his deeds may be made manifest, that they are wrought in God.
The condemnation is a refusal to abide in the light.
Here is a question for you.
Why would Paul BEG people be reconciled to God if such reconciliation HAD NOTHING to do with an act of free agency?
2Co 5:20 Now then we are ambassadors for Christ, as though God did beseech you by us:
we pray you in Christ's stead, be ye reconciled to God.
We Pray - G1189 - deomai
Middle voice of G1210; to beg (as binding oneself), that is, petition: - beseech, pray (to), make request. Compare G4441.