WARNING: THIS ARTICLE CONTAINS MAJOR SPOILERS FOR THE MASS EFFECT TRILOGY (LEGENDARY EDITION)
There were three possible Mass Effect endings, each with profound effects on the universe. In Andromeda's case, the problem was sidestepped by going so far away from it that the consequences weren't felt. There is evidence that BioWare used another method to escape the endings.
BioWare once stated that they would never canonize the ending of Mass Effect 3. This is why Andromeda did not mention the endings at all. The sequel can accomplish the same thing by making all the endings irrelevant. Probably the best way to go about that is to put it far in the future and provide straightforward reasons as to why certain events occurred.
A massive amount of evidence indicates that Mass Effect 2 takes place in the distant future
The sequel trailer shows Liara with crow's feet, something she had never had before. The Asari live to the age of 1,000, while Liara is just 106 when Mass Effect 3 opens. For comparison, Samara was a 600-year-old Asari who did not have Crow's Feet or wrinkles in Mass Effect 2. For Liara to age that much, at least 500 years would have passed.

It's hundreds of years later, but why are the relays still broken in the trailer? The relays were constructed by ancient beings who used a lot of Element Zero; each was the size of a small moon. Element Zero was still being researched during the events of Mass Effect, so it's very likely that they hadn't reached their full potential for at least half a millennium.
Finally, there's the Reaper, which proves that BioWare isn't attempting to use the third Mass Effect endings. Undoubtedly, the dead Reaper indicates the destruction ending was picked? Not necessarily. The Catalyst was used for the first time at the end of Mass Effect 3, so the all knowing Star Child from that game was just guessing at the outcome.
It could be that, after a few hundred years of being controlled by Shepard or synthesized by Shepard, the Reapers couldn't handle it anymore and were destroyed. Since they were created by a race that never could have predicted the powers of the Catalyst, it is safe to say sometimes, things break. Therefore, all three endings could result in dead Reapers.
What about Mordin and Thane? They were in the Mass Effect sequel teaser
These names have been mentioned so often when talking about this teaser picture.

They're dead, remember? They died during the events of Mass Effect 3. Those are simply individuals belonging to a race that inhabits the galaxy. Please refer to the picture below. Those two races served to remind us that those characters were dead, so that we wouldn't think these are Shepard's old friends.

How does BioWare create new games without referencing previous ones? By creating endings that all lead to the same conclusion as stated above. Don't forget that they've done endings before that are essentially the same, just different colors.
So what about Shepard?
Shepard is dead. Even in the perfect ending, because the Indoctrination Theory "isn't real," he had to have died shortly after breathing again. But isn't it strange that Liara found Shepard in the ice?
As part of Mass Effect 2's Lazarus Project, we found out that even after contact with space, burning up from return to a planet, or even impacting that same planet, we could bring Shepard back to life.
So wouldn't it be easier if Shepard was only frozen?

Here is my theory, Shepard froze. Shepard landed on a cold planet and froze or was spit out by a reaper onto that planet and froze. Either way, they have enough of Shepard to bring the Commander back to life.
That's our theory about the current plot of Mass Effect and how they are avoiding the endings. As time progresses, we will develop new theories and provide you with just as much evidence. Until then, enjoy Mass Effect Legendary Edition because it releases today!