The search can be invoked dynamically upon grid load. Just set search to true and the criteria.
<?php 
require_once '../../../../php/demo/tabs.php';
?>
<!DOCTYPE html>
<html>
  <head>
    <title>jqGrid PHP Demo</title>
    <link rel="stylesheet" type="text/css" media="screen" href="../../../../css/jquery-ui.css" />
    <link rel="stylesheet" type="text/css" media="screen" href="../../../../css/trirand/ui.jqgrid.css" />
    <link rel="stylesheet" type="text/css" media="screen" href="../../../../css/ui.multiselect.css" />
    <style type="text">
        html, body {
        margin: 0;            /* Remove body margin/padding */
        padding: 0;
        overflow: hidden;    /* Remove scroll bars on browser window */
        font-size: 75%;
        }
        
    </style>
    <script src="../../../../js/jquery.min.js" type="text/javascript"></script>
    <script src="../../../../js/trirand/i18n/grid.locale-en.js" type="text/javascript"></script>
         <script src="../../../../js/trirand/jquery.jqGrid.min.js" type="text/javascript"></script> <script type="text/javascript">         
    $.jgrid.no_legacy_api = true;
    $.jgrid.useJSON = true;
    $.jgrid.defaults.width = "700";
    </script>
     
    <script src="../../../../js/jquery-ui.min.js" type="text/javascript"></script>
   </head>
  <body>
      <div>
          <?php include ("grid.php");?>
      </div>
      <br/>
      <?php tabs(array("grid.php"));?>
   </body>
</html>
grid.php.
<?php
require_once '../../jq-config.php';
// include the jqGrid Class
require_once ABSPATH."php/PHPSuito/jqGrid.php";
// include the driver class
require_once ABSPATH."php/PHPSuito/DBdrivers/jqGridPdo.php";
// Connection to the server
$conn = new PDO(DB_DSN,DB_USER,DB_PASSWORD);
// Tell the db that we use utf-8
$conn->query("SET NAMES utf8");
// Create the jqGrid instance
$grid = new jqGridRender($conn);
// Write the SQL Query
$grid->SelectCommand = 'SELECT OrderID, OrderDate, CustomerID, ShipName, Freight FROM orders';
// Set output format to json
$grid->dataType = 'json';
// Let the grid create the model
$grid->setColModel();
// Set the url from where we obtain the data
$grid->setUrl('grid.php');

// initialsearch 
$sarr = <<< FFF
{ "groupOp":"AND",
    "rules":[
      {"field":"OrderID","op":"lt","data":"10255"}
     ]
}
FFF;
// Set some grid options
$grid->setGridOptions(array(
    "rowNum"=>10,
    "rowList"=>array(10,20,30),
    "sortname"=>"OrderID",
    // set the initila search upon loading
    "search"=>true, 
    // setr criteria
    "postData"=>array( "filters"=> $sarr )
));
//toolbarfilter sttings
$grid->setColProperty("OrderID", array(
    // the value set in filters is 10255
    "searchoptions"=>array("defaultValue"=>"10255", "sopt"=>array("lt"))
    )
);


// Change some property of the field(s)
$grid->setColProperty("OrderDate", array(
    "formatter"=>"date",
    "formatoptions"=>array("srcformat"=>"Y-m-d H:i:s","newformat"=>"m/d/Y")
    )
);
$grid->setColProperty("ShipName", array("width"=>"200"));
// Enable navigator
$grid->navigator = true;
$grid->toolbarfilter = true;
// Enable search
// By default we have multiple search enabled
$grid->setNavOptions('navigator', array("excel"=>false,"add"=>false,"edit"=>false,"del"=>false,"view"=>false));
// In order to enable the more complex search we should set multipleGroup option
// Also we need show query roo
$grid->setNavOptions('search', array(
    "multipleGroup"=>true,
    "showQuery"=>true
));
// Enjoy
$grid->renderGrid('#grid','#pager',true, null, null, true,true);
$conn = null;
?>