Paul argues that Abraham got to heaven by faith, not law. Abe was ordered to kill his son, by Elohim, so he did so. This is the type of faith needed to get to be with God.
AH, I'm not sure Paul made the case for Abraham getting into Heaven. As I have read thru the OT, I fail to see even 1 promise concerning Heaven for those who followed God's law and were considered righteous. The whole idea of a Heavenly inheritance seemed to be a new concept 1st mentioned in the gospels that was limited by Jesus to those that were considered his.
However, the synoptic gospels, written by Jewish Christians, seem to be of a view that you can get to heaven by following Jewish law in a different way.
The parable of Lazarus in Luke 16, documents a supposed case of a Jew going to heaven because he was poor and neglected:
 And it came to pass, that the beggar died, and was carried by the angels into Abraham's bosom: the rich man also died, and was buried;
 And in hell he lift up his eyes, being in torments, and seeth Abraham afar off, and Lazarus in his bosom.
The parable in Luke 16 don't mention Heaven at all though. It instead seems to reference the Hellenized view of Hades. Additionally, it never makes the case that the beggar, Lazarus, was in fact a Jew. What it does tell the reader is that in the end, the rich man found himself in agony outside of the favored position of Abrahman while Lazarus got to be in that favored position the rich man saw as his own inheritance.
In pre-Christian times, it was widely believed by Pharisees that you got to heaven, if you were righteous. The logic and scripture for these beliefs has been destroyed by time; not propagated by Pauline Christians. We have evidence of this from the Ethiopian church.
After the end of the Seluclid reign over the Jews in a post Maccabean war society, it is said that the sect of Pharisees arose as sort of a separatist group that was grass roots. This group is said to have emphasized scrict Torah adherance and unlike the priestly class Sadducee counterparts, the Pharisees advocated a literal bodily resurrection of the dead in a future Messianic "age to come" where the Jewish Messiah would reign. As far as I am aware, no mention of going to Heaven was a part of Pharisee beliefs. They seem to have believed that the Kingdom of Heaven was not in Heaven, but on Earth and would be ruled by the Jewish Messiah in the "age to come."
So yes, they did believe that admittance to the Kingdom of Heaven was granted to those (Jews) that practiced righteous, which in their eyes consisted of scrict adherance to the Torah (seeing it as divine), the affirmation of the resurrection of the dead, and believing in divine intervention in human affairs.
Christians say you can't go to the kingdom without Jesus, or unless you are a child, or unless God just decides to send you to heaven because you never heard of him, or unless you were good. There is an extensive list of exceptions.
It's quite sad how this is handled by believers. I find it hard to believe I considered myself intelligent and informed while I promoted these very ideas. I guess it was a clear case of how dogmatic convictions can cloud judgment and make one blind to reality.
As I look back and consider these things now, it becomes apparant how wrong I was because for starters, I like most believers didn't have a clue what the kingdom that those ancient Jews were referencing was very likely not the Heaven we believed in. It's almost unbelievable how many Christians don't realize how little Heaven is mentioned in the OT.
The problem is: why is Jesus telling an audience that Lazarus is a candidate for the kingdom of heaven, just because he is poor?
Great question. There really is no way to answer this other than make wild guesses. My guess is that it was written to spite those, the Jewish leaders and Pharisees that didn't accept Jesus as being the Messiah.
Maybe Jesus had to be crucified, because he was such a misleading teacher?
Back to the OP. Why did Jesus have to be crucified? What a question.
Was it because it was prophesied in the OT that the Messiah would be? NO
Was it because Jesus claimed to be the Jewish Messiah, yet those most familiar with the writings about the Messiah(s) saw him, called BS, and in keeping with the Torah laws concerning false prophets, deemed him worthy of death by capital punishment? MAYBE
Was the story a fabricated one based on an amaglamation of would be Messiahs and Jewish tradition? WHO KNOWS?