BioWare let slip some very important information regarding Mass Effect: Andromeda at a press event EA held as they prep for the launch of the game near the end of March. Simply put, there's a way the old Mass Effect games can influence the adventure in Andromeda.
According to Game Informer, during the press event BioWare revealed that at the start of Mass Effect: Andromeda players will be able to choose what the gender is/was of Shepard. For those of you not in the know, Commander Shepard was the original protagonist of the first three Mass Effect games. The choices you made leading up to the end of the third game determined Shepard's fate.
In Mass Effect: Andromeda, players will choose to play as either Sarah Ryder or Scott Ryder. So, it seems interesting that they would allow you to choose the gender of Commander Shepard, unless it plays some role in how the story unfolds or references past events.
Game Informer was completely clueless as to what role Shepard would play in the game, and noted that it would influence the story in some way but didn't know how. They tried to pressure BioWare for answers, but the developers did not go into detail, so players will simply have to wait until Mass Effect: Andromeda releases in order to find out how Shepard will affect the shape of the new game's story.
Some people in the comment section were hoping that Shepard would have some role in the development of the Ryder family while others were hoping that Shepard would make a cameo in some way. They haven't mentioned anything about importing saved games from Mass Effect 3, so I tend to doubt that the relation between the old trilogy and the new game will be anything more significant than a references to Shepard as a he/she. It would be shocking, however, if the choice of the gender of Shepard played a much larger role in the story, possibly affecting some outcome involving Scott or Sarah Ryder. That would be pretty interesting.
Others noted in the comment section that BioWare had made it clear that the original Andromeda Initiative within the Mass Effect timeline took place during Mass Effect 2, so Shepard would be alive. However, the travel time took 600 years for the Andromeda crew to get to where they were going. So they missed out on all of the events of Mass Effect 3. We don't know yet if they're even aware of what happened with the Mass Relays and the fate of galaxy. The interesting thing here is that we know that Shepard can't make a cameo in the current timeline of Andromeda. However, some gamers are curious if Liara might make a cameo since she would still be alive during the events of Andromeda. In fact, it would be kind of cool if she had a little anecdote to share about Shepard and that's why players get to choose Shepard's gender. Of course, all of that is just speculation.
BioWare has been trying to distance themselves greatly from the original Mass Effect trilogy in order to give gamers the impression that Andromeda will be a completely separate experience. So I'm guessing the Shepard reference won't be that big, but we'll find out come March 21st.