Why did the Observers choose the year 2015?

The full Invader (i.e. the Observers who hatched the invasion plan) plan was first to send 12 Observers back in time, these 12 then (unknowingly) scout history to find suitable times to invade. These 12 were told they were just studying history, and were the Observers we saw all over the place in the first 4 seasons.

With the scouting complete, the Invaders then analyzed history and found likely targets for when to invade. They have the capability to predict futures, so they applied this ability to determine the best time to invade. They found this perfect time to invade in 2015, and so they launched their attack.

This is revealed in episode S05E11, The Boy Must Live, when Windmark requests authorization to travel back in time in the present to catch the Fringe time at a time and place he knows they were. He's not allowed, as they have rules about time traveling during the time of the invasion, as they fear doing so would disrupt their 99.9999% chance of succeeding in the invasion.

This is something that is also never answered, but because I am a Bad Robot fan, I chuck up a familiar subtext to be about "fate" by telling a story of several timelines (iterations of inextricably linked universes) working towards "spiritual progress" by Blue Walter(s) atoning for all his mistakes, which is furthered by [finally] allowing blue Olivia to become a mother, with a child that gets to live in a "normal" world, but ultimately Peter is the key for this all being possible, as Peter keeps Walter(s) in check and reminds Walter(s) of his humanity...

Back to When You've Never Been - Transcript: THE OBSERVER: I came to tell you... I have looked at all possible futures... and in every one, the result is the same. (struggling to breathe) You have to die.

So even though we only ever get a "practical" reason for why the Observers need to occupy an earlier time, we never get either a practical or emotional reason for why it's this specific time in this specific timeline, but I speculate that season 4+ is the timeline the Observers were originally created in (only one set--the universes kept dying before another set could ever be made), but that it begins to get "rewritten" over with the arrival of Peter, then Olivia replacing another Olivia, and then eventually in season five, Walter is given season 1-3 blue Walter's memories back via Micheal's touch.

Note: We don't know if the season 1-3 universe went on without everyone or ceased to exist or whatnot -- nor if the future the Observers come from (in season 5) is in fact in the same timeline for season 4 and 5 and/or if perhaps the season four timelines (red/blue-amber) are the only time lines the Observers can travel in after Peter chose "Balance"

In addition, the ending provides a conundrum too, because either there would have to be a two or there was a double reset (from two points) that created two new timelines from Walter time traveling. But the fact that letter Walter already wrote gets there, may suggest that this was "suppose" to happen with or without Observer's consent and suggest there is some "missing piece" of information the audience doesn't have...

Donald (formerly September) tells Walter in The Boy Must Live, that he always loved "this era"---and so whether one interprets that to the many 2010-2040's periods which is when the previous universes kept dying (The Day We Died + Peter and the Machine) and so double sets of Observers are never created and/or it's because of watching Walter(s) becoming a father in one or several timelines inspired his journey to become a father too, it is very curious that everything would happen this way at this time, let alone the polarization of Widmark's revenge feeds back into the narrative about why the Observers were ever created, and the evolution to not just remove "negative" emotions, but all emotions...

Because it was after the merge between the two universes! They for some reason needed the two universes to become one before they could come back. (Maybe some of them were in one universe and some in the other? Or maybe the merge “changes” the universe in some way again (Walter admits that their universe crossing has changed both universes) that allows them to travel through time in mass?) The Machine is needed for that somehow, so they needed Walter and Bell to build the machine (presumably for their cross-universe studies; remember that Nina identified the blueprints for The Machine as looking like Bell’s work) and then they needed Jones to implement his plan to merge the two.

It’s currently either 2011 or 2012 in the Fringeverse. Assume that once the merge occurs it takes a few years for the universe to “stabilize” or the conditions to become right for them to do their mass time travel and invade. So 2015.

Source: http://14kofginafpd.com/posts/television/fringe-4-19-letters-of-transit/