Yes and no.
No, you can't totally reorganize the system/user/templates structure - ExpressionEngine needs the basic filesystem layout to be in place in order to work.
Yes, you can do as you please in your template directory (it looks like you are using default_site). You already have a blog.group directory, so you can make an assets.group directory along side of it to store your asset files. Any other template files you create would reference your asset files like this:
<link rel="stylesheet" href="{site_url}system/user/templates/default_site/assets.group/style.css" />
For what it is worth, I am in the habit of moving the system directory above the document root and creating a symbolic link from the document root to my template's asset directory, like so:
css -> ../system/user/templates/default_site/assets.group/css
fonts -> ../system/user/templates/default_site/assets.group/fonts
img -> ../system/user/templates/default_site/assets.group/img
js -> ../system/user/templates/default_site/assets.group/js
This makes the site a bit more secure and makes asset pathing cleaner.