Both things are true at once, which is why the argument never ends: the speaker changes a little, and you change more.
Mechanically, a new driver's suspension (the surround and spider that let the cone move) does loosen slightly with use. Manufacturers sometimes specify a running-in period, and measured changes exist. They are modest, and mostly in the bass, where a slightly more compliant suspension lowers the driver's resonance by a few hertz. Audible? Possibly, at the margin, if you were listening for it. A different speaker? No.
Perceptually, the larger shift is you. Your ears adapt to a new tonal balance over days; what sounded bright on the first evening becomes the new normal by the weekend. And in the same window your placement improves: you pull the speakers off the wall, toe them in a little, move the sofa, and each of those does more than any burn-in ever measured. So the speaker "opening up" over a fortnight is real, it is just mostly happening between your ears and your furniture.
Practical rules, then. Do not judge a speaker in its first hour. Do not return one in its first week. And do not buy any accessory that promises to burn anything in: normal music at normal volumes is the whole procedure, and it comes free with the speaker.
Where the rule stops mattering: still wrong after weeks of fair listening, with placement done properly and the AVR set up? That is not failed burn-in. That is the wrong speaker for your taste or your room, and more waiting will not fix it. Worth a frank conversation at that point rather than another month of hoping. Tell us what you hear and what the room looks like and we can usually tell which of the two it is.
Not sure what fits your room and budget? Share your room size and budget on WhatsApp. It is a two-minute answer with a floor plan.
