Right off, I have a couple questions tho:
You don’t believe Adam was the first man, but then you said:
“As the descendants of Adam, humans have one nature which can choose to do evil and one nature that can choose to do good.”
As I said before, since Adam sinned, Adam brought sin into the world. The attachment to the material world, which is sin, was inherited by the descendants of Adam.
The humans who descended from Adam have one nature which can choose to sin and one nature that can choose to do good.
That does not mean there were no humans BEFORE Adam. In other words, that does not mean that Adam was the first man who ever existed.
It only means that
Adam was the first man who brought sin into the world.
Since we all have that ability, basically Free Will, then we’re all descendants of Adam, right? So how is he not the first man?
Everyone living in this age is a descendant of Adam since they can trace their ancestry back to Adam.
Also, what is the “Adamic cycle of religion”?
In short, I believe Adam was a Prophet, the Prophet who inaugurated the Adamic Cycle of religion, also called the Cycle of Prophecy. The Adamic Cycle ended with Muhammad, who was the seal of the Prophets, since he was the last Prophet in the Adamic Cycle of religion. Being "the Seal" did not mean there would be no more Prophets after Muhammad, as God will send Prophets to mankind as long as he exists.
Baha'is believe that the Bab and Baha'u'llah ushered in a new Cycle of religion in 1844 AD, called the Cycle of Fulfillment, or the Baha'i Cycle, and that we are now living in the Age of Fulfillment since all the Bible prophecies have been or will be fulfilled during this Cycle.
Briefly, a universal cycle in the world of existence signifies a long duration of time, and innumerable and incalculable periods and epochs. There were many cycles of religion before the Adamic Cycle, since Prophets have been sent by God to humans from the beginning of human existence, which was approximately 200,000 years ago. No records are to be found concerning the Prophets that have preceded Adam, or of the kings that lived in the days of those Prophets, because of their extreme remoteness, as well as to the vast changes which the earth hath undergone since their time. Moreover, such forms and modes of writing as are now current amongst men were unknown to the generations that were before Adam.
Was there sin as we know it before the days of Adam? That is an interesting question. Mankind might have sinned but perhaps God only started holding humans accountable for sin when Adam came into the world because mankind was not spiritually mature enough to be accountable before that.