There is so much wrong with the premise to your conclusion that the Bible is false. First of all the Aboriginal and Native Americans were not contemplating the number of one man, as the verses in the Bible dealing with Jesus were. There were myriads of people listed in the Jewish chronologies, not all of them had anything to do with Jesus. Secondly when establishing the claim of Jesus' chronology not every single person in that line needed to be named. Only a few were necessary. Another point of consideration is that before the flood people, like Adam, could live up to over 900 years. Thirdly, and unrelated to chronology, just as an aside, Jesus didn't die on a cross, he died on a Hebrew torture stake. A simple upright pole. The cross didn't infiltrate Christianity until Constantine.
The only thing you got right in your post was that if Adam and original sin wasn't real then there would have been no need for a Messiah to deliver us from that sin.
Does not the Bible claim Eve to be the mother of all mankind? So the Bible is incomplete with its genealogy of 77 generations listed between Jesus Christ back to Adam who was with Eve, the mother of all mankind?
"A straightforward addition of the chronogenealogies yields a date for the beginning near 4000 B.C. Chronologists working from the Bible consistently get 2,000 years between Adam and Abraham. Few would dispute that Abraham lived around 2000 B.C. Many Christian leaders, though, claim there are gaps in the Genesis genealogies. One of their arguments is that the word
begat, as used in the time-line from the first man Adam to Abraham in Genesis 5 and 11, can skip generations. If this argument were true, the date for creation using the biblical time-line of history cannot be worked out.
In a recent debate, a well-known progressive creationist stated that he believed a person could date Adam back 100,000 years from the present. Since most modern scholars place the date of Abraham around 2000 B.C. (Ussher’s date for Abraham’s birth is 1996 B.C.), the remaining 96,000 years must fit into the Genesis 5 and 11 genealogies, between Adam and Abraham.
Now, if we estimate that 40 years equals one generation, which is fairly generous, this means that 2,500 generations are missing from these genealogies. But this makes the genealogies ridiculously meaningless."
Are There Gaps in the Genesis Genealogies?