In the event handler itself, you will then read the three drop down box values. With them, you can construct a value you will then place in the date input field. In this event you can also determine if the field is a date input that is supported by the browser or if it is not supported and change the value you place in the text input (for browsers like Safari).
I know it sounds like a lot, but it isn’t too bad. Just break the problem down. Get the event listener to work for your three drop downs first, then move on to pulling out their values and setting the date input value. Lastly then look at how you might detect if the date input is a date input vs a text input.