Upvote:2
Delta flies from Terminal 1, which is open 24 hours a day (Source: MSP website). So normal check-in times will apply.
Upvote:3
To check-in for the flight in the sense of informing the airline that you intend to board the flight and to obtain a boarding pass, you have 24 hours before departure to do so from the website or the mobile app. As Delta's Bagggage & Travel Fees guide notes, you can do so even if you plan to check bags. You check in, tell Delta how many bags you intend to check, pay any applicable fees, and then bring them to the luggage drop after you arrive at the airport.
If for whatever reason you prefer to check in at the airport, it is unlikely there will be any airline personnel at the counter before about 4am. Delta uses Terminal 1 (the Lindbergh Terminal) at Minneapolis-St. Paul International, where there should be at least one TSA screening checkpoints open at that hour.
I assume you are on DL1991. This is in fact the first flight of the day out of MSP for Delta or any of Delta's partners, and as such, the lines at the check-in counters/kiosks and at security will be quite manageable—I would say this is broadly true of the first flights of the day operated by any major U.S. airline at any domestic hub, and at the great majority of spokes.
The only anecdotal report I could find is from TripAdvisor back January 2017, which reports arriving after 4 not to be a problem.