I have months without events at all.
let's say in June there is no event at June
because we are in June today, the fullcalendar page default to June, so no event is there, it is empty.
Is there any option to default to first next month having events?
in this scenario, it would default to July as it is the first next month with event.
Unfortunately, we don't have that option available. So you will need to edit the menu item you created to display calendar, set Default Month parameter to that Month for now
When no value is set for Default Month parameter, current month will become default