Repentance is not an action of man. Repentance is a work of grace performed in man by the Holy Spirit.
That's right insofar as initial repentance is a miraculous gift from God which man cannot perform or choose by himself, so that we must be:
2 Timothy 2:25 In meekness instructing those that oppose themselves;
if God peradventure will give them repentance . . .
But note that an initially repentant Christian can still at some subsequent point wrongly employ his free will to go back to sinning without repentance (2 Peter 2:20-22). For initial repentance at the point of initial salvation (Mark 1:15, Acts 3:19, Acts 11:18, Acts 26:20; 2 Timothy 2:25) is different than subsequent repentance (or the lack of it: Hebrews 10:26-29) for sins committed sometime subsequent to initial salvation (2 Corinthians 12:21, Revelation 2:5, Revelation 2:16, Revelation 2:21-22, Revelation 3:3, Revelation 3:19).
Also, regarding the ideas of initial salvation and ultimate salvation, note that they do not have to be explicitly referred to in the Bible as "initial salvation" and "ultimate salvation" for them to be true and supported by the Bible, just as, for example, the ideas of the unity of God and the Trinity do not have to be explicitly referred to in the Bible as "the unity" and "the Trinity" for them to be true and supported by the Bible (John 10:30, John 1:1,14, Isaiah 45:5, Matthew 28:19, Acts 5:3-4).
For in the Bible, the difference between initial salvation and ultimate salvation is that initial salvation is by grace through faith in Jesus Christ without any works at all on our part (Romans 4:1-5, Ephesians 2:8-9, Titus 3:5; 2 Timothy 1:9). But other passages show that Christians must have both faith and continued works of faith (1 Thessalonians 1:3, Galatians 5:6b, Titus 3:8) (not works of the letter of the Old Covenant Mosaic law), if they are to obtain ultimate salvation (Romans 2:6-8, James 2:24, Matthew 7:21, Matthew 25:26,30, Philippians 2:12b, Philippians 3:11-14; 2 Corinthians 5:9, Hebrews 5:9, Hebrews 6:10-12; 2 Peter 1:10-11, John 15:2a; 1 John 2:17b). For Christians must continue to do righteous deeds if they are to continue to be righteous (1 John 3:7, James 2:24,26). And there is no assurance that Christians will choose to do that, instead of wrongly employing their free will to become utterly lazy without repentance, to the ultimate loss of their salvation (Matthew 25:26,30, John 15:2a).
Also, in the Bible, the difference between initial salvation and ultimate salvation is that initial salvation is the salvation which Christians have now (Ephesians 2:5), in their mortal bodies, while ultimate salvation is the salvation ready to be revealed in the last time (1 Peter 1:5), and which is always drawing nearer (Romans 13:11), that salvation which Christians are still hoping for (1 Thessalonians 5:8, Romans 8:23-25, Mark 10:30), and which Jesus Christ will bring to obedient Christians at His future, Second Coming (Hebrews 9:28, Hebrews 5:9), when He will resurrect (if dead) or change (if alive) their mortal physical bodies into immortal physical bodies just like the immortal physical body which Jesus obtained at His resurrection on the third day after His death (Luke 24:39,46; 1 Corinthians 15:3-4,21-23,51-53, Philippians 3:21, Romans 8:23-25, Philippians 3:11-14).