Initialize search input in jQuery Datatables

The proper way is now:

var table = $( '#mytable' ).DataTable();
table.search( 'initial search value' ).draw();

So the proper way of doing this is using the oSearch parameter.

https://datatables.net/docs/DataTables/1.9.0/DataTable.defaults.oSearch.html

$(document).ready( function() {
  $('#example').dataTable( {
    "oSearch": {"sSearch": "Initial search"}
  } );
} )

You can trigger an event manually with .trigger():

$('#example_filter label input[type=text]')
    .val('Default Product')
    .trigger($.Event("keypress", { keyCode: 13 }));

Depending on your code, you may want "keyup" instead.