The old links to a top level page converted to a child should still work. If a page “bar” is made a child of page “foo”, example.com/bar/ should still take us to example.com/foo/bar/. Of course if there are duplicate child names under different parents, the first matching page found will be returned even if it’s not under the intended parent.
If you are not getting this behavior, try visiting the permalinks setting screen, which causes the rewrite rules to be regenerated. Probably will not help, but it’s easy to try.
See if it’s due to theme interference. Try using Twenty Fifteen without the child. If still no joy, deactivate all plugins as well. Solo child links ought to work now. Narrow down the cause of failed links by restoring child and plugins, one at a time until the links again fail.