Can every single sound ever made(from the beginning of time) be recreated again? Sound is a wave and energy decreases as $1/r^2$ . The intensity of sound is proportional to $(amplitude)^2$ of the wave. 
So if we amplify the wave with some instrument then we can hear every single word ever spoken in the history, can't we?
But the thinking part seems quite simple.. and I don't know of something like this existing so I guess that I am wrong. But why am I wrong? 
 A: First, energy decreases as $1/r^2$ only in 3D space (compared to the span of the wave volume), assuming heterogeneous condition (not like mirages, for instance. Plus as large scales atmosphere is stratified, or can even be considered 2D). 
Second, you neglect damping: some energy is lost, and worse, diffused, blurring the message. The lost part is transformed into heat, that you can also interpret as motion. 
Indeed temperature agitation creates a "thermal noise", that fortunately our very good perception is just one magnitude over perception (probably not a coincidence). So all weak signals will be lost in the noise.
You also neglected dispersion, i.e. difference of speed with the ton. In air there is almost no dispersion, but at huge scales of time I won't bet too much.
So, no, you can re-decode past sound.
A: Fabrice NEYRET's answer is good, let me just add another point of view.


*

*Nonlinearities: the first thing that occurs when any nonlinearity must be taken in account is that linear superposition is not valid any more. Therefore is really tricky (if possible) to distinct sources of superposed waves.

*Signal processing: I simply can't think of any algorithm capable of reconstruct signal in time domain as a reverse engineering when more then a few sources and a few reflections (not to mention refractions etc.).

*Thermodynamics: In many applications acousticians believe in "law of entropy conservation" which is very useful approximation but of course generally wrong. And then refer to the theory of thermodynamic processes reversibility.

*Chaos and turbulence: Don't forget that actually many sound producing mechanisms are not (fully) deterministic (e.g. vortex sound production in a turbulent field) and hence there is no simple rule-like way to treat them reversibly.
