No verse in Scripture claims Eve gave birth to Cain after the Garden, any more than you claim what I see as wrong. You see what you want to see.
Can you prove when Cain and Abel were born? No you cannot. Seth was born when Adam was 130. You have no proof any more than I do that it could have been over 100 years between births. Normally people do not wait until they are 130 to have offspring. You claim Eve and Adam had Cain and Abel on the 6th day in Genesis 1:26-28, no? They also sinned the next day, no? Can you explain how Seth was born 130 years later, instead of the day after Cain killed Abel? How old were Cain and Abel in chapter 4? Was Seth born the next day?
"And Adam knew Eve his wife; and she conceived, and bare Cain, and said, I have gotten a man from the Lord."
This verse does not say anything about after leaving the Garden. But notice this:
"And in process of time it came to pass, that Cain brought of the fruit of the ground an offering unto the Lord."
This story had at least 128 years "to come to pass". Let's assume procreation worked even better than it does today, well in fact it did:
"Unto the woman he said, I will greatly multiply thy sorrow and thy conception; in sorrow thou shalt bring forth children"
You really think Adam waited until after he disobeyed God to procreate with Eve? Once again:
"And Adam said, This is now bone of my bones, and flesh of my flesh: she shall be called Woman, because she was taken out of Man. Therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they shall be one flesh. And they were both naked, the man and his wife, and were not ashamed."
Nothing in there about being celibate. Chapter 4 could have easily started out after chapter 2 chronologically. How would Eve know a difference in child bearing if there was no pre-disobedience child birth?
The process of time in Genesis 4:3 very well could have included the events in Genesis 3.
Genesis 3 was literally only about Adam's disobedience and nothing else. It was not a necessary chronological event preceding Genesis 4. Genesis 4:25:
"And Adam knew his wife again; and she bare a son, and called his name Seth: For God, said she, hath appointed me another seed instead of Abel, whom Cain slew."
Adam was given Seth 130 years from some starting point. There is really no indication that Adam left the Garden at 129 years. I think Adam left the Garden 100 years before Seth was born.
I think Adam was placed in the Garden 130 years before Seth was born. There was a 30 year span where chapters 2 and 3 played out. I also think chapter 4 happened in a way that those words "in the process of time" included part of those 30 years. God indicated that Eve already experienced birth and that it would be a lot different the next time. So in 100 years how much sorrow did Adam and Eve have before Seth was born? If you claim they were in the Garden for over 100 years, exactly what happened during that time? If you claim they left the Garden 130 years before Seth, what was the process of time needed for between Cain and Abel growing up with no one around? Are you saying Cain was a tiller of the ground as soon as he could walk? Is being a tiller of the ground prohibited in the Garden of Eden? Adam and Eve were now in dead corruptible flesh. That was prohibited in the Garden lest they continue to eat of the tree of life and live forever in sin and dead corruptible flesh. Did not God kill an animal in the Garden to cloth Adam and Eve?
"Unto Adam also and to his wife did the Lord God make coats of skins, and clothed them."
Nor does it ever say that Cain and Abel made sacrifices for sin.