Interesting question. I am not an atheist so I cannot answer for them but I have known people to offer different explanations. A Catholic co-worker suggested to me that it was trial and error. A lot of people feel that way. But that only raises more questions that it answers.
Trial and error, how? Were the boys dying? At what age? And if they were dying, was it ten minutes into the procedure, twenty minutes after the procedure? Or perhaps a day later? Let's say Daddy did it on the third day - three is a nice number. What would alert Daddy to something being wrong? Did the little tyke bleed to death? How did Daddy know that's what did it? Mayhap the little tyke got a hold of some rust off of the knife. Did he bleed only heavy and not die? Did he get maybe a little listless. Lethargic? Low blood volume will do that.
Suppose Daddy picked day seven. Another nice number. Did the same scenarios happen? If it did, how often? How many baby boys died? Ten? Twenty? Forty-eight? Three hundred? What about when twin boys were born? Did Daddy circumcise one on the second day and one on the fifth?
Vitamin k - the blood-clotting agent - is at its highest on day eight. So it is all about the blood-clotting cascade effect. To suggest that man came up with the eighth day by trial and error is, first of all, to acknowledge that the eighth day is the best day. And then one is also acknowledging that all the daddies circumcised their boys on the eighth day.
What does that mean? It means everybody seems to accept that it was done on the eighth day, everybody seems to accept the eighth day as the best day but when it comes to God telling them the eighth day, that's where everybody bows out and hands off to 'trial and error.'
Trial and error is not a viable explanation. It is not reasonable to contend such when we follow through to logical and illogical conclusions.
Hannah J Paul