According to the 2K rep, because the game was completed prior to the NBA finalizing the schedule for the current season, there was no way to have it ready for launch since the entire feature is connected to the real NBA ledger.
As far as adding it as a post-release update, 2K cannot commit, though it appears they are looking into it. The rep said: “It would be a major effort to retroactively support it on a live product with live saves and all that.”
It makes sense, though I seem to recall comments about the new schedule being patched in, so I figured Start Today would've been activated by that. In any case, the disruption and late start to the season mean that the Start Today option is up in the air, and may not end up being a thing this year.