I thought of another similar situation. Table is 5 handed, they have been told by the floor to keep going. The last hand has already ended. The dealer is in the middle of his shuffling sequence, people are still chit chatting, texting on their phones, etc. the dealer finishes his shuffle, and is about to put out the cut card and call for antes and blinds etc. At that moment, players from a broken table arrive.
I would guess that most TDs would have the players seated, post the antes and blinds, and continue the hand with a full table.
If we interpret "the hand begins with the first riffle" as meaning the entire hand must be played out with all the same players who were at the table when the riffle occurred, no more and no less, then technically we should wait until that whole hand is played out before the players from the broken table could be seated to resume play. I don't think that is practical. We also want the players from a different table to resume play as soon as possible. Just because the hand has "begun" for the purposes of identifying the applicable blind level, doesn't mean we cannot remove or add players to the hand before the cards are dealt out, IMO.