Daily Challenge mode is an optional side mode, you have to progress a bit the main game first. You can’t access Simulation Mode (Daily Challenge mode) from start.
To unlock Daily Challenge, you must make it through the first biome in the Returnal: Overgrown Ruins. This also means defeating the boss Phrike.
After defeating Phrike, continue playing and When you reached the Helios crash site – enter into the ship ( this is a safe zone ).
In the central room, you will find two monitors. The smaller one in the corner gives you access to Simulation Mode, which is the Daily Challenge mode. Approach the monitor, press Triangle to get it.
Note: To get the Platinum Trophy, you will need to play this mode at least once to unlock the Trophy In-Field Training.