So the answer is pretty simple -
running streamer into DAC (try to set up a playlist consisting of music with different bit rates and set it on repeat) without your amplifier on: you’re breaking in the digital in, power supply and the DAC section. You’re not breaking in the output section. To do a full end to end break in your amp or preamp that DAC is connected to has to be on. You can choose to break in the analog out section while listening and keep the digital front end running 24/7 with amp off and it will take a few days more. The digital section and power supply break in will be typically around 200hrs.
Or bite the bullet and keep the amp on for few days. When amp is off the signal from DAC analog out is not flowing.