The quoted texts, Acts 5:31, 11:18, 2 Tim 2:25, are among many that teach this same idea, namely, that salvation is entirely God's initiative. Here are some more: Phil 2:13, John 6:44, Rom 2:4. Therefore, repentance, confession and conversion are not things we offer to God but our response to His pleading and prompting!!
Let me state this more strongly, Salvation is a free gift (Rom 3:20, 4:6, Eph 2:5, 8-10, Gal 2:16, Tit 3:5, Isa 64:6, Acts 4:12, etc) and decided upon by God before the world began (Matt 25:34, Heb 4:3, Rev 13:8). Thus, there was a plan to save sinners before there was a sinner! Such a plan was created without consulting any human. Further, this plan was initiated to demonstrate God's justice and righteousness (Rom 3:25, 26). Therefore, repentance is not a work we do to earn salvation - it is God's initiative (Acts 17:30) not ours.
The salvation that came as such a shock to the Jews, was that it was universal and included Gentiles. This idea is repeated numerous times in Scripture:
- John 1:29, “Behold the Lamb of God who takes away the sin of the world.”
- John 3:16, “God so loved the world that He gave …”
- John 12:32, “I [Jesus] … will draw all people to myself.”
- Acts 17:30, “God … commands all people everywhere to repent.”
- Rom 3:23, 24, “… for all have sinned … and all are freely forgiven...”
- Rom 5:8, 10, “… while we were still sinners, Christ died for us. … if, while were God’s enemies, we were reconciled to him by the death of His Son, …”
- Rom 5:15, “But the free gift is not like the offense. For if by the one man’s [Adam’s] offense many died, much more the grace of God and the gift by the grace of the one Man, Jesus Christ, abounded to the many.” [Note the same word, “many” applies to all people.]
- Rom 5:18, “Therefore, as through one man’s offense judgment came to all people, resulting in condemnation, even so through one Man’s righteous act the free gift came to all people, resulting in justification of life.”
- Rom 11:32, “For God has imprisoned everyone in disobedience so that He may show mercy to all.”
- 2 Cor 5:14, “…we are convinced that one died for all, and therefore all died.”
- 2 Cor 5:18, 19, “…God was reconciling the world to Himself in Christ …”
- 1 Tim 2:3, 4, “For this is good and acceptable in the sight of God our Saviour, who desires all men to be saved and to come to the knowledge of the truth.”
- 1 Tim 2:6, “[Jesus Christ] gave Himself as a ransom for all people.”
- Titus 2:11, “For the grace of God appeared bringing salvation to all people.”
- Heb 2:9, “But we see Jesus, who was made a little lower than the angels, now crowned with glory and honour because he suffered death, so that by the grace of God he might taste death for everyone.”
- 2 Peter 3:9, “The Lord is not slow in keeping his promise, as some understand slowness. He is patient with you, not wanting anyone to perish, but everyone to come to repentance.”
- 1 John 2:2, “He Himself [Jesus] is the propitiation for our sins, and not for ours [Christians to whom John writes] only but also for the whole world.”
- Isa 53:6, “We all like sheep have gone astray … and the LORD has laid on him the iniquity of us all.”
The Bible frequently makes this same point of wanting to save all people by emphasising that God does not show favouritism but treats all people impartially (Duet 10:17-19, 2 Chron 19:7, Ezek 18:25, Mk 12:14, Acts 10:34 Rom 2:10-11; Eph 6:9, 1 Pet 1:17).