Depending on what you are looking for, there can be multiple solutions. If you want to move the crop rectangle and ensure it aligns with the edge, try placing a guide at the left edge, the crop rectangle should stick to it when moved freely. Another option mentioned is using selection. There is a setting in the options bar to define selection dimensions in advance before drawing or creating it. Later, use free transform selection to move it to the edge, using the guide as an anchor, or change the anchor to the left edge and then type 0 (zero) for the X position (screenshot below).
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