Blog in one folder, files in another?

I’m planning on making some big changes soon (like upgrading to 2.0), and one of them is to make my blog my site’s home page (right now it’s in a sub-folder of the main site; my blog is https://www.badastronomy.com/bablog, but I want my blog page to come up when you go to just https://www.badastronomy.com).

But I don’t want the WP files littering up my top “public_html” folder. Is there a way to make the blog index.php page my main page, but still keep all the support files and folders (info.php, wp-content, etc.) in a sub-folder?