Photo Resizing to square composition without distortion

It sounds like JJMack’s solution is the one you want. Below is what the steps would look like. If you want white borders, then while you are in the Canvas Size dialog box, choose White as the Canvas Extension Color as shown below. Using the Fit Image command means it will work regardless of the dimensions, proportions, or orientation of the original, so it works great for batch automation. 

Use the Crop Tool.

Set crop height and width to 1080 x 1080.  See screenshot.

You would use menu File>Automate>Fit Image... set 1080 PX is width and Height.  to resize the image to fit within 1080x1080 canvas size then use menu Image>Canvas Size...  Un-check relative and set  wirth and height 1080 px to add any missing canvas boarders will be added if required.

I'd make a new file 1080x1080 and then drag the photo over into it and move it around till it looks good. I looked at the shoes image, and I can see right away you have room at the top and the bottom that can be cropped off. You can't just resize a rectangle into a square without some distortion,