I was thinking something along these lines. I've already paid a little visit to ZU and some of them over-analyzing the time travel aspect of SS by saying that the events of the ending already happened before the beginning of the game, which doesn't work out
How does it not work out? The ceremony that Zelda and Link had at the end of the Wing Ceremony is based off of the one that the Goddess and her chosen hero had... which later in the game, in the past, after Zelda is revealed to be the Goddess Reborn and Link is the Goddess chosen hero they had the ceremony. What about the bracelet that Zelda gave to Impa and that Ancient Impa had since the first time Link meet her how she seems to know more about what is going to happen? Actually she talks a lot about the wheels of fate, how it is Link's fate to save Zelda and save the world, and how it was all destined long ago... like she personally knows what is going to happen like she already saw the events of the game from young Impa's eyes(which would make sense since she is young Impa... except that she is no longer young anymore.)
Also what would happen if the events in the game didn't already happen? The seal on Demise in the past would have failed long before Zelda and Link were born because Zelda wasn't lead to the past to go into the slumber that would strengthen the seal to last till Zelda and Link were born. So Demise is free, based on the fact that Hylia isn't anywhere in the Past when Link and Zelda was there(and you must admit that she would have come if she felt Demise breaking free of her seal.) and also because Demise mentioned that only Link stand between him and the Triforce, Hylia has already started the "incarnation into mortal form" so technically she is dead. And there is no hero is coming since none of the humans at that time is brave enough to fight Demise... So Demise would have found a way to Skyloft and slaughter the rest of the humans, thereby making it impossible for there to be a Link or a Zelda in the "present" that would have gone into the past to stop him.
Let's look at it from one last view. Impa, she was ordered by the Goddesses(most likely right before she starting her incarnation.) to go into the future to lead Zelda to the past. If there is one thing that we know from OoT it is that the events that would play out while a character is in stasis will still play out so she should, by logic of the events of the ending not happening before the game, landed in a time where Demise is free and has control of the Triforce(because of the above 'paragraph'.), but she did not because the events of the ending happened while she was in "stasis".
and that the Master Sword was sealed behind that door in the temple the whole, never mind the fact that the pedestal is right behind the Gate of Time.
You mean the same pedestal that does not appear in the past until after Demise is defeated? If it could appear out of nowhere then it could disappear and reappear again.
My guesses for that are A) Zelda gave Impa the bracelet in the past to see if it was her in the present, or B) it was an error on Nintendo's part, and you really don't see it unless you really pay attention.
You should really watch the ending again. Zelda gave it to Impa believing that she would not see Impa again. And based on how important they based that reveal on the bracelet it is most likely not an error on Nintendo's part.