You should be able to disconnect the water supply lines to the sink at the angle stop valves on the wall, and disconnect the drain line at the trap or trap adapter, then pull the sink cabinet away from the wall.
I have attached an illustration for a simple method of making an access hole for inspection.
It would be impossible to offer a time estimate until the actual point of the leak is located.
Normally the water will dry inside the wall unless there is evidence that the sheetrock is saturated. In that case you may have to cut out the saturated sheetrock and replace it.
