FileZilla cannot do that.
You have to use another FTP client, if you need such feature.
I do not know about any FTP/SFTP client that allows arbitrary multi-selection on its "site manager".
But for example with WinSCP SFTP/FTP client, you can organize the sites to folders (just as with FileZilla) and you can open all sites in a specific folder at once.
And you can of course specify an initial folder to browse to:
Note that WinSCP actually only opens a browser with tab for each site in the folder, and connects only the first (active) site. The other sites are automatically opened once you switch to their tabs.
Also note that once you have the main browser window opened, you can reorganize the sites as you like, sort, add new, remove others, etc. And then you can save your resulting site-set as a workspace (kind of a virtual site folder).
And you can have WinSCP automatically import your sites from FileZilla.
(I'm the author of WinSCP)