This can be a very scary question for children growing up in covenant homes. They cannot remember a time that they didn't consider themselves a Christian, a follower of Christ. If their parents have been consistent in their covenant upbringing, they have never known a time that their parents refused to bring them to the Table as covenant members of Christ. They were small saplings and there may not have been fruit, but only because the branches were too small to hold any. But that is no reason not to feed the sapling and believe that it will grow up and bear fruit - and as covenant parents to do all you can to make that as easy and natural (or supernatural) as possible.
We do not have to have Damascus road type conversions in order to know that we are saved. Timothy was taught the Scriptures from his earliest recollection, raised as a covenant member from the beginning. Douglas Wilson is fond of saying you don't have to know what time the sun rose to know that it is up (Wilson, AC, p71).