How long does a DAC take to burn in?

100 hours ! Industry unspoken standard! No true set time! I call it " till it pops " Reproduction seperates and stages! I.e.: life like sound!

I think only speaker drivers open up or burn in...the rest is probably you getting used to the sound.

Nitewulf has very good point and is probably on the right track in my experience.  The mind is very powerful and automatically starts filling in gaps and frequency observations while listening to familiar music.  

Not true especially with a Loudspeaker crossovers ,and Teflon dielectric high purity wire , Teflon dielectric takes over 400 hours before the music is much smoother with capacitors without question the higher the quality like Duelund, Jupiter,Jensen , Millflex very tightlly wound foils,and dielectric .
many people say 6he bigger Duelunds, and Vh Audio Teflon capacitors 500 hours. , the majority of speakers use Cheap,or inexpensive build quality
like Solen capacitors  which only take 100 hours vs the $$ high quality caps .
i spent 20 years having or modding for others. And documented listening and comparing using several people in testing .the key is the quality of  parts used.

Many DACs sound better with 24/7 on.

They do not consume lot of power unless it has a vacuum tube in it.