For the Finals MVP prediction I think picks should be submitted by the start of the first Finals game: Your finals MVP is basically your finals pick 90% of the time anyways and usually you have one team you favor going into the series even if you're uncertain.
For regular season picks I guess it depends how soon awards are announced. If none of them are announced before the playoffs you could just say they're all due by the first game of the playoffs, or just the day before any of them are announced all picks are due. With the MVP race, even if you can make a very legitimate argument for one player their chances of winning might be diminished by their team record or lack of narrative, so by the end of the season it's usually narrowed down to 3 candidates at most, with one being the odds on favorite from either a stats or narrative(or both) standpoint; the other awards usually have a little more of a randomness element, maybe 1 is a lock ahead of time, but it usually feels like a semi legitimate competition compared to the MVP selection. The general NBA discourse usually does a pretty good job of acknowledging legitimate cases for awards(with the exception of the MVP of course); If you've watched throughout the season, kept up with the discourse for at least the last portion of the season, and done whatever amount of research you deem necessary, you can usually narrow down your selection by the close, or near the close, of the season.