Though there is no direct evidence for Adam and Eve having existed, this does not necessarily make the belief irrational. In principle, it may be supported by indirect evidence (if one holds to a religious belief, itself well supported by evidence, that implies the historicity of Adam and Eve). Either way, current science tells us little about whether Adam and Eve plausibly existed.
The historicity of Adam and Eve is a question which strikes at the heart of the Christian faith. If the primordial pair did not exist, then the historical and biblical doctrine of the fall becomes extremely difficult to maintain.
Some may wonder why I have chosen to address this topic prior to engaging with other topics (such as the meaning of the ‘days’ in Genesis 1). I have done so because many young earth creationists consider this to be the more pressing concern, and perhaps even the strongest argument for their position from Scripture.