However, a thief cannot receive instant salvation without accepting the first principles and ordinances of the gospel, which include repentance and baptism.
Janderich, the passage has been understood that the thief repented by accepting their punishment…and by asking and knowing that they were asking God incarnate for eternal life by believing in the Son. Baptism here is by desire and does not limit God to a baptism by water, as the Pharisees limited God by holding to the Law.
In 2 Corinthians 12 below, paradise is being described as heaven in the same way as how Luke uses it with the thief on the cross.
1 I must boast; not that it is profitable, but I will go on to visions and revelations of the Lord.
2 I know someone in Christ who, fourteen years ago (whether in the body or out of the body I
do not know, God knows), was caught up to the third heaven.
3 And I know that this person (whether in the body or out of the body I do not know, God knows)
4 was caught up into Paradise and heard ineffable things, which no one may utter.
5 About this person I will boast, but about myself I will not boast, except about my weaknesses.
6 Although if I should wish to boast, I would not be foolish, for I would be telling the truth. But I refrain, so that no one may think more of me than what he sees in me or hears from me
7 because of the abundance of the revelations. Therefore, that I might not become too elated, a thorn in the flesh was given to me, an angel of Satan, to beat me, to keep me from being too elated.
8 Three times I begged the Lord about this, that it might leave me,
9 but he said to me, “My grace is sufficient for you, for power is made perfect in weakness.” I will rather boast most gladly of my weaknesses,* in order that the power of Christ may dwell with me.
10 Therefore, I am content with weaknesses, insults, hardships, persecutions, and constraints, for the sake of Christ;e for when I am weak, then I am strong.
Also in revelation 2, paradise is used again in the same way = tree of life = heaven. KJV below
7 He that hath an ear, let him hear what the Spirit saith unto the churches; To him that overcometh will I give to eat of the
tree of life, which is in the midst of the paradise of God.
Tree of life…Revelation 22
1 And he shewed me a pure river of water of life, clear as crystal,
proceeding out of the throne of God and of the Lamb.
2 In the midst of the street of it, and on either side of the river, was **there the tree of life, **which bare twelve manner of fruits, and yielded her fruit every month: and the leaves of the tree were for the healing of the nations.
3 And there shall be no more curse: but the throne of God and of the Lamb shall be in it; and his servants shall serve him:
The tree of life is in front of the throne of God (in heaven) which is the same as being in the midst of the Paradise of God.