Break in for new DAC

As for your question I'm a +1 too with  @bigtwin - don't let burn in get in the way of exploring and enjoying the music. Does the new DAC emotionally engage you more is a great place to start, then if it does the whys? Some break-in is necessary with new electronics and tubes. I was advised up to 500 hours with my Denafrips Venus 15th, which does seem excessive, but it did open-up noticeably after 400 hours, why I frankly don't know!

My approach with new kit is to compare directly the new with the old through your player - not sure if Vinyl, CD or Streaming setup? If I'm replacing a component I usually have reasons like I'm looking to change the sound and synergy between components, preferably to the better.  With a new DAC I'd be looking for things like comparing soundstage - depth, width, instrument positioning. Retrieval of details at different frequencies and with tubes for those high transients and midrange. So if you can it is interesting to compare and take notes about what you hear or don't hear between new and old. Usually you're looking for more from the sound, as an audiophile colleague says to be lifting away the veil that was there before :)

Burn in is kind of like cables-an unresolvable debate. My ears are fine and my gear is fine and I've never noticed much change in new electronics during any "burn in" time. Speakers, things with moving parts may be a little different-mechanical devices. That's just my experience. If someone else has a different experience-whether its the electronics or their brain that is burning in-I wouldn't take issue. Its foolish to try to tell someone else what they hear, even though its often tried.

What can you do if the sound of a product changes during burn in until it reaches perfection to your ears, but then it keeps burning in and keeps changing in a suboptimal way? Logically, that would happen since we all have different tastes and ideas of what constitutes the sonic optimum and you would have no way to stop the burn in at precisely the right time.That would be frustrating.

The good thing about burn in, unlike cables, switches, crystals, etc., is that it doesn't really matter which side is right. If burn in really happens, you can't stop it. If it doesn't, you can't force it. Nothing to buy, or not, so all is well. Unless you hang on to something that doesn't sound good beyond the return date. Don't do that.

At any rate, it happens or not without any intervention from us, so no use getting the nasties over it. Smart people on both sides of this one.

Life's a biartch and then you die.

does the amp really need to be on?

Few have addressed this point.  The DAC does push some electricity towards the amplifier, and the amplifier presents as a load to the DAC.  So why not create an equivalent dummy load from resistors just in case electrons really can create a burn-in effect?

I am reminded of a radio skit from John Cleese and others, about a letter to an Agony Aunt in a women's magazine:

Dear Marge

I am worried about my son.  He is growing something in his window box which he says is cabbage, but I think is marijuana.  What should I do? Yours, Worried.

Dear Worried

try some and if you are still worried, it's cabbage

Generally speaking, most equipment needs break-in to sound best, in my own experience.  200 hours or more for your DAC would not seem unreasonable to me, which will happen naturally over time as you use it.  I would not leave the tube equipment on for that long just to burn in the DAC.