Yeah but there's no precedent for that technology to exist in a pre-ME3 galaxy. On the contrary, the previous games have made it explicitly clear that intergalactic travel isn't possible with the current level of technology in the universe. Ships can't travel more than 50 light years without discharging, and this is cited as one of the big barriers for space expeditions INSIDE the galaxy, without the use of Mass Relays. Sure, with the Mass Relays there is no commercial need for such tech, but wouldn't space expeditions invest in it to increase their range? Of course they would, but because they haven't, the technology obviously isn't available.
Could they pull new, shiny tech out of their asses to solve this inconvenient problem? Of course, but that would be spitting on a narrative credibility that's already coated in seven layers of spit.
If they instead set the starting point of the journey several centuries AFTER the Reaper War, they are able to write in the necessary technological breakthroughs in the intervening centuries and make it perfectly believable. But knowing BioWare, they will go with the dumbest possible premise imaginable. It's not even funny how inept these guys have become where storytelling is concerned.
"We have no choice but to try" isn't a statement about the Reapers. We wouldn't be fleeing the Reapers on the basis of an insatiable curiosity - that would make absolutely no sense. The message is directed to us as human beings in a meta sort of way, not an in-universe message to a hypothetical crew of the Ark. The "For our fear" part is definitely a reference to the real-life fear that life as we know it will be destroyed when our sun grows so hot that Earth can no longer sustain life. The only way to escape that fate is to leave the solar system and find another, younger (or slower aging) solar system that has a planet that can sustain Earth-based life.
The last four lines are basically a message from the original trilogy, embodied by Shepard, saying goodbye to us and basically telling us we'll have the good memories of Mass Effect 1-3 going into Andromeda.
The only thing in the N7 "teaser" that can be even remotely connected to ME:A is the design of the intergalactic ship and the interior shot of the cockpit with the Ryder dogtags. The rest is just space nerd NASA archive footage fanservice packaged with some ME-CGI as a love note saying "Please, consumer-kun, take me back and we'll start over ~uguu".
This is Mass Effect we are talking about. Do you think it matters if ME1-3 stated intergalactic travel wasn't possible at the time? Look at the reapers. It's space magic. Space voodoo. Half of the nonsense that happened in the games wasn't based on some in-depth understanding of the laws of science. Drew Karpyshyn, the lead writer on ME1 and ME2, even admitted a lot of this stuff was space magic and purposely mysterious in order to draw interest and appeal. Not everything, including intergalactic travel, needs to be explained.
ME3's ending was already controversial enough. Do you really think the writers wouldn't take creative liberties just to avoid dealing with that ending? Come on. Andromeda was an excuse to not deal with the Milky Way. Of course there was no intergalactic travel at the time because the writers didn't think ME3's ending would blow up in their faces.
Except, by still staying in the Milky Way centuries later, they still have to explain the endings. If the ARK launches between ME2 and ME3, which the teaser trailer suggests, they can completely avoid dealing with ME3 entirely.
I bolded the parts that suggest this move could have been partially motivated by the reapers. Again, as someone else stated earlier, Andromeda could have already been in development and was re-purposed with an accelerated time table to escape the reaper invasion. As far as your comparison towards our sun becoming a super nova, highly unlikely. That won't be happening until billions of years from now and Mass Effect does not take place that far into the future from current day.
I really don't believe this is a message to the audience, which you seem to believe. I think this is entirely a message to the crew of the ARK. We even have the dog tag with the name "Ryder" on it, which many suggest is the new protagonist's surname.
I think you are being overly-critical and letting the marketing campaign of the game get in the way of the actual message. Again, reasonable minds may differ, but I think there is a lot more to this teaser than you realize. We'll find out soon enough, but it's seems quite likely the ARK departed the galaxy before the reapers arrived to invade Earth.