Definitely getting server date is not possible without querying server.
So do a separate AJAX call to get the server date, or if your application already sends some ajax query, place the date in Date
header in server-side, and read it in client.
Also if you entire page is served dynamically (like PHP), place server side date in html source like this:
<script>
var serverDate = <?= time() ?>
var dateDiff = new Date - serverDate;
</script>