How to extract the first dimension in TimeSeries?

You can also use TimeSeriesMap or MapAt:

audio = AudioLocalMeasurements[ExampleData[{"Audio", "PianoScale"}],"MFCC"];

res0 = TimeSeriesMap[{First@#}&, audio]["Path"];
res1 = MapAt[{First@#}&, audio["Path"],{{All,2}}];
res0 == res1 == res

True

You can use the "Properties" specification of a TimeSeries, as introduced in the Details section of its reference page. This avoids normalizing it.

For instance, with the properties "Times" and "Values":

audio = AudioLocalMeasurements[ExampleData[{"Audio", "PianoScale"}], "MFCC"];

res = Transpose[{audio["Times"], audio["Values"][[All, {1}]]}];

The symbol res gives the expected output:

data = Normal@audio;
res === Thread[{data[[All, 1]], data[[All, 2, {1}]]}]
(* True *)

Alternatively, you can use the property "Path". Here is a possible way:

resBis = {#1, {#2[[1]]}} & @@@ audio["Path"];
resBis === res
(* True *)

Note that other objects of the language accept the "Properties" specification, once they are constructed through evaluation. These include SparseArray and QuantityArray:

spa = SparseArray[Range[10]];
spa["Properties"]
(* {"AdjacencyLists", "Background", "ColumnIndices", "Density", "MatrixColumns", 
    "NonzeroValues", "PatternArray", "Properties", "RowPointers"} *)

qa = QuantityArray[Range[10], "Meters"];
qa["Properties"]
(* {"Data", "Properties", "Structure"} *)

The specification "Methods" can also be used for these two last:

spa["Methods"]
(* {"AdjacencyLists", "Background", "ColumnIndices", "Density", "MatrixColumns", 
    "MethodInformation", "Methods", "NonzeroPositions", "NonzeroValues", "PatternArray", 
    "Properties", "RowPointers"} *)

qa["Methods"]
(* {"Data", "MethodInformation", "Methods", "Properties", "Structure"} *)