The DCIM folder is part of the industry standard for camera-based file systems.
DCIM is short for Digital Camera IMages and is part of the industry standard outlined by the Design rule for Camera File system. This standard was adopted as the de facto standard for storing digital image and sound files in memory devices by the digital camera industry to insure interoperability from one brand to the next.
Design rule for Camera File system (DCF) is a JEITA specification (number CP-3461) which defines a file system for digital cameras, including the directory structure, file naming method, character set, file format, and metadata format. It is currently the de facto industry standard for digital still cameras. The file format of DCF conforms to the Exif specification, but the DCF specification also allows use of any other file formats.
Further, many cameras refuse to display images taken with different cameras, particularly those from different manufacturers that can vary the way the 'maker notes' section of the EXIF info is structured even when those images are inside a properly named folder within the DCIM folder.
In fact, many cameras, including all I've seen from Canon, will not display images taken with that same camera if certain portions of the EXIF info have been changed or removed using another device, such as a computer. Some cameras will no longer display an image if something as simple as the orientation has been rotated ninety degrees with a program using a computer, rather than with the camera's menu.
These examples are all the case when the images are loaded back into a properly named folder within the specified DCIM convention.
Any files in folders outside of the Design Rule for Camera file system will not be acknowledged by any camera of which I am aware.
The problem with this is that after I've backed up the recent photos, I don't always want to erase them from the camera but rather want to put all existing media in a separate folder so I know what's already been backed up to store/cloud.
Although you can't see it in the interface, if you use Canon's download utility to transfer files to your computer, it does place a flag in the 'maker notes' section of the EXIF info of the file. The next time you use the Canon image transfer utility, if you instruct it to only transfer "new" images, it will not transfer previously transferred images again. There's no need to move the images anywhere.
If you insist on using other methods to transfer images I suppose you could create a new DCIM\nnnXXXXX folder¹ and set the camera to save to that folder following the transfer and know that images in all except the newest folder have been copied to your computer, assuming you don't go over 9,999 images in that folder before transferring them to your computer. All Canon EOS cameras have this capability. I'm not sure about the SX620.
¹ Where n is a numeral between 0-9 and X is an alphabetic character between A-Z or an underscore. Folder names are actually required to be in this specific format for Canon cameras. By default Canon uses 101CANON, 102CANON, 103CANON, etc., but with most newer EOS cameras you can custom create folders with other names, such as 101AAAAA, 102AAA_B, etc. There can only be one folder with each three digit numerical combination at the beginning of the folder name. You can have both a 101AAAAA folder and a 102AAAAA folder, but you can't have a 101AAAAA and a 101AAAAB folder at the same time.