web sitene şöyle embed edebilirsin

<iframe src="https://docs.google.com/forms/d/e/YOUR_FORM_ID/viewform?embedded=true" width="640" height="480" frameborder="0" marginheight="0" marginwidth="0">Loading…</iframe>

Web sitene form submit olayını yakalayıp çalıştırabilirsin

<script>
    document.addEventListener('DOMContentLoaded', function() {
      var iframe = document.querySelector('iframe');
      iframe.onload = function() {
        var form = iframe.contentDocument.querySelector('form');
        form.onsubmit = function(event) {
        alert('Form submitted!');
          
        };
      };
    });
  </script>