By CPT (or better: the Chess version thereof) if a game is opened by Black, you can transpose it to the standard version (by swapping board, colors and move rights) and there is no visible difference. I somewhere read that the Immortal indeed was played this way. I googled a bit, it seems that the convention that White begins was first proposed by master Löwenthal, i.e. is not that old at all!
Can a historian help out about a) when "White moves first" was canonized worldwide (pre-1st version of FIDE rules?) and b) if the Immortal indeed was played with Black moving first?