Could mother Eve have children before the fall?
While yet in the Garden of Eden, Eve was named based on the promise of her motherhood (Moses 4:26, Genesis 3:20). The realization of this promise could not come until after the Fall when Adam and Eve entered mortality.
2 Nephi 2:22-23 teaches the nature of their existence in the Garden of Eden:
22 And now, behold, if Adam had not transgressed he would not have fallen, but he would have remained in the garden of Eden. And all things which were created must have remained in the same state in which they were after they were created; and they must have remained forever, and had no end.
23 And they would have had no children; wherefore they would have remained in a state of innocence, having no joy, for they knew no misery; doing no good, for they knew no sin.
After the Fall, when Adam and Eve learned of the Plan of Salvation, Eve rejoices in their promised future:
“And Eve, his wife, heard all these things and was glad, saying: Were it not for our transgression we never should have had seed, and never should have known good and evil, and the joy of our redemption, and the eternal life which God giveth unto all the obedient.” (Moses 5:11)
These verses not only teach that Adam and Eve were unable to have children before the fall, but also that the physical state of everything prior to the fall was unchanging. The ability to bear children is one of the blessings of mortality, and clearly Eve recognized and rejoiced in this.
The Atonement does more than merely restore us to that paradise which before was lost, for eternal increase is the blessing of the faithful (D&C 131:1-4, 132:19-24). It’s akin to our before/after states when passing through probation. Before this life we were in the presence of God. After this life we will again be in His presence, if faithful. We will have improved though. We will have mastered these elements that we call a body and will be like God in that respect. And (most relevant to this question) we will be parents, the title which God applies to Himself!