I think that it would be a good idea to add drop-down lists to select day/month/year for easier navigation.

For example, in the month view, two drop-down lists could be added, one to select the month to be viewed and another to select the year.

According to https://docs.moodle.org/36/en/Using_Calendar:

Navigating months

There is no easy way to jump to a specific month in the year other than to directly edit the URL variable for month "m=" : calendar/view.php?view=month&cal_d=1&cal_m=02&cal_y=2006

Drop-down list should resolved this.