Auto Submit Contact Form 7

You need to call submit() function on document ready
check the code

<script type="text/javascript">
jQuery(document).ready(function(){
     jQuery("#wpcf7-f3857-o1 form").submit();
});
</script>

In my code wpcf7-f3857-o1 is the contact form’s css id.
You need to change that id.
try the code and let me know the result.
Thanks