Was Elvis ambitious?
 

Was Elvis trying to become famous before 1955, or was it something that just happened without him intending it to?

every musician wants no one to hear them.

I think he was trying to establish a career as a country singer, but never expected it to get as out of hand as it did.

depends on how you define 'trying to become famous'

he'd been performing for years and already recording for a couple before '55 so... yeah it seems rather clear that he was in fact trying to make a go of things.

Does anyone not try to become famous? Even if they are not expecting it, or counting on it, who actually puts effort into being mediocre?

Mediocre isn't really the opposite of famous at all.

yeah there are plenty of people who don't try to become famous. you won't hear about them unless you're friends them though, it's kind of how obscurity works.

out of all the people i know who play music i'd say it's around a 50 / 50 split from those who want to accomplish 'something' with their music and those who honestly don't give a crap and just play for fun with friends.

I think, like any musician, Elvis simply wanted to become successful at his chosen career, but the level of success and fame that he achieved may have only been a dream to him pre-1955.

I'm going to say yes, every musician is trying to be famous if they have a chance.

No.