lol guess who's going to die at the start of your game? (theoretical spoiler?)

How does ME:A fit?

You hail from humble origins...

Well, the dad has accomplished a bit, but the bro and sis are relatively fresh. Loosely fits the cliche.

A devastating battle sends your quiet life spinning out of balance

Disaster on approach to Andromeda or soon after arriving (I say 90% certainty). Strongly fits the cliche.

The attack leaves you with two companions, of magical and martial prowess

Liam (Combat)
Harper (Biotic)
The sibling may also be available.
Either loosely or strongly fits the cliche.

Undaunted by the attack, you recover and are swiftly invited into an elite order that places you in a position of power or authority over the rest of humanity

You are promoted to pathfinder. While your 'power' is unknown, your importance is vital. Loosely or strongly fits, depending on your role on the station.

You discover that you must travel to four main locations in order to save the world/galaxy

Seven 'golden planets' are mentioned, but what you actually visit is unknown.
Not enough info

With your mission well under way, your every effort is thwarted by an evil or sinister organization

The role of the alien races are yet to be seen, but at least some will be very hostile. I say that it is more than likely you will have fierce political critics on the Nexus. I would not be surprised if Cerberus shows its face. 
Not enough info, but very likely. 

At some point, you fall asleep and there is a dream sequence

I'd bet on some nightmares with Archon.
But not enough info.

Further along in your journeys, you discover the ruins of a sprawling ancient civilization

Not enough info. I say unlikely, since you are discovering sprawling current civilizations. But those civilizations may have killed off some others.