Hello Yuval,
I think that the only way to do this is by making a change to the database. You need to add an entry to the sys_page_compose table which corresponds to the event calendar in the index page, in order to accomplish this.
I recommend backing up the sys_page_compose table before applying the following insert query. This query should work for you:
INSERT INTO sys_page_compose VALUES(NULL, 'index', '998px', 'Event Calendar', '_bx_events_calendar', 2, 1, 'PHP', 'bx_import(\'BxDolService\'); return BxDolService::call(\'events\', \'calendar\', array());', 1, 50, 'memb', 0, 0)
After the query, clear the cache. You can modify settings by going to the Page Builder for the index page, from the administration page. Hope this works for you.
Regards,
kazatzo