I did a little digging to see where else in Scripture Paul may have been thinking when he wrote this reprimand to the Corinthians and to all of us. I found this:
The secret things belong unto the LORD our God: but those things which are revealed belong unto us and to our children for ever, that we may do all the words of this law. (Deut. 29:29)
That sounds right. Do you think so, too? In other words, we can't possibly know ALL there is to know, nor could our brains process it all, but what we ARE accountable for is what God has revealed to us in His holy word. The New Living Translation puts it this way:
The LORD our God has secrets known to no one. We are not accountable for them, but we and our children are accountable forever for all that he has revealed to us, so that we may obey all the terms of these instructions.