This lesson is only possible for versions no lower than UniTheme 1.4. In order to display on your site a menu that is open by default for the main page, you will need layouts file (download it).
Before you will do any changes for your store - please make a full backup (to have a chance to restore it, if something will go wrong).
In the admin panel of your store go to (Design > Layouts) and make a new layer [+] Add new layout.
Make all needed settings for layout and save it:
Then select the newly created layout (UniTheme - FixedMenu) and import into it the previously downloaded file of ready layouts.
In the opened popup (Import layout) choose downloaded file. Check option (Update current layout) and (Override locations by dispatch).
Press button (Import) and your layout (UniTheme - FixedMenu) for homepage will be updated. Now you will have opened menu for main page.
Note: after you will update you layout you will need to reconfigure your blocks for main page and meta tags.