Plot your inquiries by hour and look for a peak nobody staffs
The first useful exercise is not a page redesign, it is a chart of when people try to reach you.
Export your calls, forms and messages for the last ninety days and bucket them by hour and by day. Read what the chart shows rather than what you expect it to show. If a real share of your inquiries lands outside office hours, that is the finding, and it decides what happens next.
An evening or overnight cluster is the round the clock economy showing up in your data. Hospitality, healthcare and casino operations run continuously, so part of your market is free at hours your phone is not.
You do not have to staff every hour. You do have to decide what happens in each one: a live answer, an answering service with a script you wrote, or an immediate text back that sets a time.
Do the same chart for missed calls specifically. The overlap between when people call and when nobody picks up is the cheapest problem you will find all year.