Hide navigation menu on page load using jQuery

I'm using the theme Divi from Elegant Themes and I am trying to hide the main navigation menu when the page loads. I then would like for the menu to load as I scroll as seen here (http://ift.tt/1E2B15t)

I've successfully been able to have the menu appear and reappear as desired after I scroll down then back up to the top of the page. I have this as my current jQuery funtion:

<script type="text/javascript">
    jQuery(document).ready(function($) {
        var header = $('#main-header');
        $(window).scroll(function () {              
            if ($(document).scrollTop() == 0) {
                header.removeClass('et-fixed-header');
            } else {
                header.addClass('et-fixed-header');
            }
        });
    });
</script>

This is the CSS for that section:

#main-header { -webkit-transition: all .5s ease-in-out; -moz-transition: all .5s ease-in-out; -o-transition: all .5s ease-in-out; transition: all .5s ease-in-out; }
.home #main-header { opacity: 0; top: -40px !important;}
.home #main-header.et-fixed-header { opacity: 1; top: 0 !important; }
.home.et_fixed_nav #page-container { padding-top: 0!important; }
.et_fixed_nav #page-container { padding-top: 80px !important; }

I have everything labeled in the html appropriately, but I can't figure out how to make the menu not show initially. I've tried to use this, but I'm guessing I'm doing something wrong:

    <script type="text/javascript">
        jQuery(document).ready(function($) {
            var header = $('#main-header');
            $(document).load(function () {
                header.removeClass('et-fixed-header');
            $(window).scroll(function () {              
                if ($(document).scrollTop() == 0) {
                    header.removeClass('et-fixed-header');
                } else {
                    header.addClass('et-fixed-header');
                }
            });
        });
    </script>

I'm new to jQuery and a novice at WordPress development...

Thanks in advance!