Sorry, a nice thought, but not quite right. Actually "The First Time" is no exception at all. The tune was played on the 'ZOOROPA' Tour 1993, when the album was new in the shops, too.
It was performed along with "Numb" (full band version), "Stay" (full band version), "Zooropa" (cut short full band version), "Babyface" (full band version), "Daddy's Gonna Pay For Your Crashed" (short acoustic band snippet) and "Lemon" (very short snippet, only a line) on this European leg of the tour. The snippeted "The First Time" was a regular replacement of "All I Want Is You", when the band performed "Bad" back then – and remained in that sport right until the last show in Dublin '93, when "Bad" was played for the last time on the tour.
So the real surprise 2005/06 was, that U2 opted for dusting off this tune again from their shelves and performing it acoustic and complete. But this is another story ...