According to Wikipedia, Halo: Combat Evolved took about five months to crack 1 million copies:
"by April 8, 2002, a little under five months after its release, one million units had been sold".
The later games in the series did this much quicker (Halo 2 had more than 1 million pre-orders) but looking at new IP shooters, Splatoon seems to be one of the strongest launches we've ever had.