Mormons give the priesthood to men whose fathers are not Mormons.
Jesus was not the father of his Apostles, nor was Paul the father of the many Elders he ordained. There was a new way to obtain the priesthood, by oath or ordination.
Cain's first sin was undoubtedly committed before he killed his brother.
Probably so but he was cut off from the Lord for murder,
"....and ye know that no murderer hath eternal life abiding in him." 1 John 3
There is no evidence that Adam and his sons, including Cain, held any priesthood.
Gen 4
3 And in process of time it came to pass, that Cain brought of the fruit of the ground an offering unto the Lord.
4 And Abel, he also brought of the firstlings of his flock and of the fat thereof. And the Lord had respect unto Abel and to his offering:
To make an offering someone had to have the priesthood.
Note: Mormon god failed in his goal and put a roadblock in front of black Africans and their descendants.
No he actually made it easier and a point of the gospel you must have never learned;
Jacob 2- 3, he is directing this at the sinful Nephites but lets place Cain and Enos children into the mix;
Behold, ye/Enos' children have done greater iniquities than the Cainites , our brethren. Ye have broken the hearts of your tender wives, and lost the confidence of your children, because of your bad examples before them; ......neither shall ye revile against them because of their filthiness/sinfulness ; but ye shall remember your own filthiness, and remember that their filthiness/sinfulness came because of their father Cain.
Wherefore, ye shall remember your children, how that ye have grieved their hearts because of the example that ye have set before them; and also, remember that ye may, because of your filthiness, bring your children unto destruction,
and their sins be heaped upon your heads at the last day."
The Bible also teaches "Therefore to him that knoweth to do good, and doeth it not, to him it is sin" James 4:17 and Rom 5 :13 (For until the law sin was in the world: but sin is not imputed when there is no law...."
The principle is if a man's father is a bad example and teaches him to sin then his sins will be placed on the head of his father. So all of Cain is a son of perdition meaning all of his children's sin are placed on his head because he was a bad example. Laman and Lemual are also sons of perdition, their childrens sins are placed on their head.
Their children's judgement day will not be as hard as Eno's children who were taught the gospel and had the priesthood.
In the 138 sec of the Doctrine and Covenants President Joseph F. Smith sees into the spirit world and all of those who never heard of Jesus in this life being taught the Gospel and says they are "heirs of salvation". Many many LDS black people today are doing their genealogy, going to the Temple to do the baptisms and then sealing husbands and wives together forever.
They are not being denied eternal life at all.