Gravitational waves from the big bang may be "heard" but not by LIGO. The waves emitted at or around the inflationary epoch of the big bang are expected to be at much lower frequencies (milli-Hz or lower) than those announced today by LIGO. There are various sources of noise that make LIGO insensitive to GWs at frequencies below about 10 Hz.
It will take space-based interferometers like the proposed LISA, with longer interferometer arms and well away from terrestrial sources of noise to stand a chance of detecting such GWs.
If they are detected - they might "sound" something like this (if upshifted into the audible range) - from the LIGO website. It sounds like white(ish) noise because of the broad continuum of frequencies expected.
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