Is it possible that Cain and some other children were born in the Garden before Adam sinned? I am going to say no.
Why do I say this?
Imagine Adam and Eve in the garden before sin. They experienced for a time the best marriage between a man and a woman ever in the history of the world. Their bodies were the most fit for reproduction and there was nothing slowing them down from getting pregnant on their honeymoon.
Let's pretend for a moment that sin did not occur for ten years after they were created and married. Their son Cain and his eight or so brothers and sisters by that time would be playing tag, hide and seek, or some other game that kids play in a perfect jungle-like garden.
One could argue that all of the kids would be with mom and dad at the tree when Satan was tempting Eve, but given the serious lack of Scripture and thinking about the reality of little-kid-syndrome, I don't think their could ever be a serious case presented for the possibility of it actually happening in that way.
If they had kids before the fall, then because of their amazing ability to reproduce, it would almost be a guarantee that one, if not both of them, would be holding a baby in their arms during the temptation. I feel that any parent would know that Satan would have had a much harder time convincing Adam and Eve to sin if they were each holding one of their little ones and looking them in the eyes knowing that if they do this they will be responsible for their death.
So let's imagine Cain was around ten years old when mom and dad ate the fruit. His brothers and sisters would have been younger and would have varied in age range. If this were the case, then all of the children would not have become sinners at the same moment Adam and Eve did. In fact, it would have even been possible for none of the children to ever become sinners.
How can I say this? Everyone born of Adam is a sinner. No exceptions!
Well, not if we try to add children into the account timeline before sin. Then we would have one exception.
The reason for this is because their [Adam and Eve's] eyes were opened when they ate the fruit. Yes, Cain and the other children were from Adam, but if some were already born then they would not have been in Adam because they weren’t in Adam at the time of disobedience which means that they would not have been in Adam when Adam died. They would have possibly been playing on the other side of the Garden at that point and wouldn't have realized the death of their parents until later that evening.
If they did have children, don't you think they, as two of the most loving parents to have ever existed, would have refused to bring their children down this path of sin and death? They would have done everything in their loving power to protect them from the separation they now knew to be their own reality.
We are sinners because we are in Adam. Meaning, when he sinned we sinned simply because we were still in him. If he would have died physically that day then you and I would never have existed, but if Cain and several other children were already born and in the world at this point, then if Adam would have died physically they would still have remained alive physically because they were no longer technically in Adam. The same is true spiritually.
It would be absurd to say that some of their children were on the other side of the Garden while mom and dad were eating the fruit and then all of a sudden even the children immediately saw that they were naked and felt shame…as if the spirit of sin just somehow made a great leap over to possess the children for an action they had no part in. If this were the case, then the children would not be ashamed at the sight of their sin (because they had not yet sinned) but at the sight of their parent's sin.
Therefore, we have confidence that Adam and Eve had never experienced the birth of a child until after sin entered into the world. Thus, the famous temptation between Satan and Eve happened very quickly. Logically speaking, it almost had to have happened at some point within the first nine months and even more likely it was probably within the first few weeks, which would make since in the beginning of chapter four just after being kicked out of the Garden they find out they are pregnant with their first child and they name him Cain.
As you can see, the argument that people put forth about Adam and Eve possibly having children in the garden before they sinned crumbles when it is placed on trial.