I need your opinion before I take it to dealer for inspection.
When accelerating from about 5 - 10 mph to 40 and above the engine or CVT emits a very distinct rumbling sound. Even more, I can feel steering wheel and gas pedal trembling as soon as I hear this sound.

Before driving Lancer I used to drive Toyota Corolla, older 2002 Lancer and some other vehicles. None of them was as noisy as this when accelerating.
Sometimes it sort of "warms up" and the noise becomes less prominent and annoying.
I do not think this is normal. Am I right?

 

definitely isnt normal. bring it to the dealer. take advantage of your warranty.