Amplify signal with extremely low S/N-ratio
Of course you can amplify the signal but in doing so you will also amplify the noise. I'm guessing that is not what you want.

Fundamentally if you want to measure a signal of similar magnitude to the noise you have to know something about the signal. The more you know about the signal the more you can design a system to measure it while reducing the impact of the noise.

If you want more help you are going to have to give us more information about your signal.