We could spend a lot of time exchanging historical data, and I’ll try to stick to the Word of God, just for this space’s sake.
The thief in the cross could not have gone to paradise with Jesus that day, and lets assume that he died (though the scriptures don’t say that)
But I’ll assume he died, since you already believe it as a fact. Jesus himself did not go to paradise that day, he just went to hell (which literally translated is sheol, or tomb, or grave to describe the state of the dead), and his going to paradise did not happen till Sunday, on the day that he resurrected.
Jesus himself, speaking right after his resurrection, said he had not gone to His Father yet.
John 20:16-17 “Jesus saith unto her, Mary. She turned herself, and saith unto him, Rabboni; which is to say, Master. Jesus saith unto her, Touch me not; for I am not yet ascended to my Father: but go to my brethren, and say unto them, I ascend unto my Father, and your Father; and [to] my God, and your God.”
Here Jesus himself said that he had not yet ascended to his Father. This is after he resurrected. So Jesus himself did not go to paradise the day he died, unless you consider the grave paradise, and if you do, why would he tell Mary he had not yet gone to his Father?
Jesus allowed his disciples to touch him after he had presented himself to his Father by going to heaven.
John 20:27 “Then saith he to Thomas, Reach hither thy finger, and behold my hands; and reach hither thy hand, and thrust it into my side: and be not faithless, but believing.”
The Scripture then is obvious, the statement to the thief on the cross is a typo of translation when you look at the scriptures in the right context. If we read it in the original context of the language,
Jesus said “Verily I say unto thee today, shalt thou be with me in paradise.” (future reference)
With this in mind, we can clearly see that after Jesus died he did not go to paradise till after he resurrected on Sunday, somewhere between the time he saw Mary and the time he saw the Apostles. And he did not lie to the thief on the cross either. The simple fact is that according to Jesus’ own words is that he had not gone to paradise that day. The thief simply died in Christ and its awaiting his second coming in the dust of the earth just like all the saints that will resurrect in that great day (1 Thessalonians 4:16).