Make a custom Video Mode for 1080x720 (matching the frame rate of your original video)
Open your 640x640 clip, and it will look something like this.
You can use the Crop:Source tool to make it fit the width of the new resolution which will look something like this depending on what you want to crop from the original clip.
Stretching a video like this will probably make your video look distorted.
By default Shotcut expands the video/picture to take up either the nearest width or height, even with sources less than the Video Mode dimensions. Applying the Size and Position filter to Fit shows the true size of the source.