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No, not really. The URLs on your site are controlled by the menu items in Joomla. Unless your site's Home menu item is your blog you cannot do what you have in mind.

Let me give you a practical example. In my blog site (https://www.dionysopoulos.me) the Home (default) menu item is an Articles, Category Blog item. This is why you do not see /blog/ being part of my posts' URLs. In the past I did have a different home menu item and my blog was under a Blog menu item so all those articles were /blog/something. When I rebuilt my site I made that menu item the default to avoid having the /blog/ in the URL. In my case it makes perfect sense because the blog is the main feature of my personal site. If this is not true in your site you cannot avoid the /blog/ part of the URL.

That said, the URL does not matter anymore. It plays no role in search engine indexing and browsers – currently Google Chrome and Safari – have already started hiding it by default.

If you want to create memorable URLs for sharing content you can of course use the URL redirection feature in Admin Tools to create a shorter, memorable URL. It will, however, be redirected to the full URL, including the /blog/ bit you dislike, upon visiting it.