Hmmm... I know I'm redeemed and that one day I will be like Him. But I find it hard to say that now, nearly 50 years after my salvation, I am any closer to being like Jesus than I was the day I was saved. I think the matter of progressive sanctification is most easily resolved when we consider that the old man is corrupt and cannot be reformed (requiring grace) and that the new man is "created according to God, in true righteousness and holiness" (Eph 4:22-24).
Read this passage...
3 Blessed be the God and Father of our Lord Jesus Christ, who according to His abundant mercy has begotten us again to a living hope through the resurrection of Jesus Christ from the dead, 4 to an inheritance incorruptible and undefiled and that does not fade away, reserved in heaven for you, 5 who are kept by the power of God through faith for salvation ready to be revealed in the last time.
6 In this you greatly rejoice, though now for a little while, if need be, you have been grieved by various trials, 7 that the genuineness of your faith, being much more precious than gold that perishes, though it is tested by fire, may be found to praise, honor, and glory at the revelation of Jesus Christ, 8 whom having not seen you love. Though now you do not see Him, yet believing, you rejoice with joy inexpressible and full of glory, 9 receiving the end of your faith—the salvation of your souls.
10 Of this salvation the prophets have inquired and searched carefully, who prophesied of the grace that would come to you, 11 searching what, or what manner of time, the Spirit of Christ who was in them was indicating when He testified beforehand the sufferings of Christ and the glories that would follow. 12 To them it was revealed that, not to themselves, but to us they were ministering the things which now have been reported to you through those who have preached the gospel to you by the Holy Spirit sent from heaven—things which angels desire to look into.
[The New King James Version (1 Pe 1:3–12). (1982). Thomas Nelson.]
To me, "the inheritance" relates to these things I have underlined above. We see glimpses of what's to come when we observe the genuineness of our own faith in Christ that is tried by fire and our deep love for Him that causes us to "rejoince with joy inexpressible and full of glory". These things are inside us because we have Jesus, the Creator and our Savior, living in our hearts and, as a result, the new man has been made in His image and is one spirit with Him (1 Cor 6:17). The prophets wrote about these things happening to us, but they never experienced it themselves. And the angels look at Christ living in us and us being one spirit with Him and they are filled with wonder, not knowing how this is possible and what it might mean. But we experience it.
3:1 Behold what manner of love the Father has bestowed on us, that we should be called children of God! Therefore the world does not know us, because it did not know Him. 2 Beloved, now we are children of God; and it has not yet been revealed what we shall be, but we know that when He is revealed, we shall be like Him, for we shall see Him as He is. 3 And everyone who has this hope in Him purifies himself, just as He is pure. (1 Jn 3:1–3)
This passage is related. We are His children (i.e., His offspring) right now. We know that we "will be like Him" one day and that we will "see Him as He is". But we don't know exactly what it means that "we shall be like Him" because God has not yet revealed those details to anyone. Therefore, what awaits us (i.e., our inderitance) is for now simply a sure hope that has yet to be revealed.