Honestly, you seem to just be criticizing usual fiction elements in general. I mean, let's go ahead and criticize the FTL tech in Star Wars universe, which physically doesn't make much sense. Let's criticize it how in Fallout 3 a green person with no experience gets out of the vault for the first time, and suddenly knows how to fight the most dangerous enemies post-apocalyptic America has to offer, topples powerful factions...
This is fiction, things are supposed to not be entirely believable. In fiction, characters meet each other by pure accident, survive countless fights in which just one bullet could put them down, defeat evils entire armies couldn't defeat, etc.
Yes, we find the plans on Mars conveniently. Yes, we easily build Crucible which countless civilizations before us couldn't. Yes, Reapers don't attack Citadel right away (which any reasonable invasion force would start with), which would immediately nullify our chances. This is fiction, you shouldn't expect it to be perfectly logical and sensible.
Reapers can't be defeated legitimately, without a deus ex machina. If the writers went with the most logical scenario, then the game would be over a few minutes after the news of the Reaper invasion reaches us: they would target Shepard and Citadel first and foremost, and with death of Shepard and loss of Citadel everything would be over. But, as you understand, it wouldn't make for a good story.