Joe Malone got the longest consecutive goal-scoring streak from start of NHL career with 14 games in 1917-18 season (NHL's first season). I guess that should be somewhere around the record, if it isn't the record.
In more modern times, I remember that Alexander Ovechkin got the record for a #1 overall pick with points in first 8 games.
Now he's at nine games and the streak is still alive.
Did players technically count as rookies in 1917-18?
Many of them would have had long careers in other leagues prior to the NHL starting that season.
Was it Malone's first year?
That's a great question!
Later, for example Gretzky wasn't rookie for that very same reason - He played in WHA. Now-a-days for example vast majority of Russians are 100% professional before coming to NHL, still they are rookies.