Something like this should work (though there will be no audible sound in the case of your data since it is just a straight line) -- note that the timeseries data is of the form

{{t1,a1},{t2,a2},...,{tn,an}}

rather than the reversed form that you gave.

So with this understanding and your date example one does

timeSeries = TimeSeries[
  Transpose[{{0.0001, 0.0074, 0.0147, 0.0220, 0.0293, 0.0366, 0.0439, 
     0.0512}, {0.0006, 0.0407, 0.0808, 0.1210, 0.1611, 0.2013, 0.2415,
      0.2816}}]
  ]

and then

ListPlay[timeSeries, SampleRate -> 1000]

Here is a different example with random amplitudes at random times:

times = Flatten[{0, Sort@RandomReal[{0, 5}, 100], 5}] 

randomTS = 
 TimeSeries@
  Table[{times[[i]], 10 RandomReal[{-1, 1}]}, {i, 1, Length[times]}] 

ListPlay[randomTS, SampleRate -> 8000] 

Here another version using Play. Imagine you got an analytic function:

f[t_] := Sin[440 2 Pi t Sin[10 t]]

It is easy to play it:

Play[f[t], {t, 0, 1}]

Now if you do not have function but just irregularly sampled data:

data = {#, f[#]} & /@ {0}~Join~RandomReal[1, 10000]~Join~1;
Short[data]
(*{{0,0},{0.366519495348991`,0.749201172621884`}, ....,{0.19676826435559214`,-0.8154545405493382`}}*)

you can recreate sound closely using Interpolation given that sampling is detailed:

g = Interpolation[data, InterpolationOrder -> 0];
Play[g[t], {t, 0, 1}]

Note sound is different but close enough.