My nigh on 50 year experience with hifi says there is a thing we could call ‘burn in’, but it’s complicated. 
This Ares had the strangest sound when I first plugged it in, interesting, enticing, but plain weird, all over the place really, disjointed maybe? But I’ve been around audiophilia long enough to know people don’t make components to sound like that - this is a a case of warm up required - mine and the DAC.
Now I reckon there are several reasons for the ‘burn-in’ phenomenon and which is topmost depends on the item - digital, analogue, bog standard op amps, chipsets, or more esoteric discrete components - and the individual involved.
The first is system acclimatisation, I often feel a new component needs time to shake hands with the rest of the signal path for a while, shift some electrons around the place, align structures - say hello! Don’t laugh, I introduce my components gently, system synergy is all, I know it works! 
The second is simply heat, atoms vibrating, components alter after warm up. Digital much less so, analogue elements more so. Even a few minutes after switch on makes a difference, my Mojo came on song about half an hour after receiving a signal, my little Topping L30 about a few minutes, my Topping E30 instantly. This Ares was ice cold on arrival, weeks in storage and transport probably, never switched on since manufacture - poor thing! I gave it some Woodward electricity (albeit not conditioned and probably terribly noisy - my speakers pop when I turn a light on!) and left it to warm up for a few hours.
The third is the most important - the personal and uniquely individual human physical and mental perception mechanism. If you listen to a component in your system whilst you are ‘burning it in’ you are actually burning in your ear/brain perception mechanism as well!! There is no way to avoid this on first listen, I found the Ares so weird because I have had several months of my existing system burning in my perception mechanism - and this now sounded very, very different.
You see, we don’t hear music, we interpret sound waves moving in the air and hitting our ears via a sophisticated ear/brain interaction. There is no music coming out of these speakers, or running down the speaker wire, or whizzing around inside the DAC or amplifier - we turn sound waves back into music via perception. We do in fact turn all reality (which is nothing more than a wave) into what we perceive it to be via the same mechanism - but that’s another story.
So if we allow the ear/brain perception mechanism loose on our new pet too early we will be simultaneously hoping the physics does it’s job, whilst also seriously interfering with the mechanism we will be later using to measure the results! And is that mechanism foolproof, absolutely not, it’s all down to perception and perception is all down to our very own learned personal filters - it’s a miracle we actually agree on anything! 