Transform + Auto scale to new Document

After I shoot a product photo, I am using quick selection tool to select only the product, click refine edge, cut + paste into new document that must be 2000 x 2000 pixels white background. When I paste into that new document ofcourse that the image cut before it is bigger than the size of the new document ( 2000x2000 ). Is there a keyboard shortcut to automatically transform to the scale of the new document ? I am using Ctr + T, hold Shift and drag picture from corners. But I am asking for a shortcut to do that faster. I have hundreds of photos.

Thank you ! Best regards.