To add a Date Picker in Magento 2 System Configuration, follow these steps:

1. Create Block

Create a DatePicker.php file in app/code/Vendor/Module/Block/:
  
<?php

namespace Vendor\Module\Block\Adminhtml;

class Date extends \Magento\Config\Block\System\Config\Form\Field
{
    public function render(\Magento\Framework\Data\Form\Element\AbstractElement $element)
    {
        $element->setDateFormat(\Magento\Framework\Stdlib\DateTime::DATE_INTERNAL_FORMAT);
        $element->setTimeFormat("HH:mm:ss"); //set date and time as per your need
        return parent::render($element);
    }
}

2. Create System.xml

Add the below code to your system.xml file
  
<field id="customdate" translate="label" type="date" showInDefault="1" showInWebsite="1" showInStore="1">
    <label>Customized Date Field</label>
    <frontend_model>Vendor\Module\Block\Adminhtml\DatePicker</frontend_model>
</field>