I have never had any problems with building the SoL as the US. I even build it in NYC, just so it feels right. So, here is what I do while playing as the USA. Criticism is welcome, of course
What I do is use all of my initial gold into building either Forges or Libraries. Your initial civics are alright for now, you might want to use your first turn (which is kind of dead anyway, as you only own Washington) and switch to either Commonwealth or Occupation (I have never switched to Imperialism, but I think it works if you want to conquer Mexico). You might wanna queue your tech research towards Industrialism and Mass Media, as to be amongst the first with the knowhow as to build the Pentagon, UN and Empire State.
In any case, do that and try to acquire Quebec, either by diplomacy, a Congress (if you don't get called for said congress, which would be odd as you would be an influential civ, try again by loading a new save. the RGN can be a bastard sometimes. in any case, you should ask for Quebec and you will get it 4 out of 5 times.) or by war. Personally, I try to avoid warring with the French, but if you see no other choice...
While you are doing that, move some of your troops to Toronto and crush the British forces there. Thus you will secure Quebec's copper from any British raid from that side.
From there on out, just keep an eye for an incoming GP and keep playing as you like. You should get one, and if you did build forges before Libraries your chances of getting a GE are quite considerable. If you do not get one, even if the odds were in your favor, reload. A GM could be acceptable, if you have the means to transport him to a city where he can get you some gold as to rush the wonder. But I wouldn't recommend it. So yeah, trust the RNG and reload if necessary. Rush the SoL by using the GE and wait a couple more turns. It shall be built before you even know it (even quicker if you did secure the copper).
The SoL will help you immeasurably. Use the momentum and, if you have spare gold, rush troops and buildings/upgrade existing infrastructure/build troops as to expel the Euros from North America. The barbarians that will spawn now and then can be easily defeated with a couple of Minutemen. The Mohawks might annoy you if you do not chop down all the forests you encounter. Chop them down however (and get some nice hammers by the way) and they will be cannon-fodder.
Some might disagree with my strategy though, but I think it kind of works. Then again, you rely on luck so it's up to ya really...