Contact Form – Date – start selection a week later

there are nice plugins to influence datepicker f.e.: Datepicker by input

but you can insert that snippet to your child-theme functions.php
( if you get rid of those outcommented signs “//” – the weekends will be unavailable too ):
( there is a prebuild option for no Weekend)

function my_datepicker_defaults() {
?>
<script type="text/javascript">
window.addEventListener("DOMContentLoaded", function () { 
(function($) {        
    $.datepicker.setDefaults({
        // beforeShowDay: $.datepicker.noWeekends,
        minDate: "+7d",
        maxDate: "+12m",
    });          
}(jQuery)); 
}); 
</script>
<?php
}
add_action('wp_footer', 'my_datepicker_defaults', 20);

if you do not need maxDate remove that line