Why is there gauge freedom in ADM formalism?

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In ADM formalism there are evolution equations only for spatial metric and extrinsic curvature, but nothing about lapse and shift. I understand that the latter two are essentially just choice of coordinates. However, if I already choose coordinates, shouldn't be their evolution also be determined? Unfortunately, all I found was that there are "gauge conditions" for this (https://arxiv.org/pdf/gr-qc/9412071). How can i determine the gauge from my choice of coordinates? Also, are ADM equations depend on gauge?
 

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