Follow the below steps to generate invoice PDF & save it on the server at invoice creation time.

1. Create file event.xml on app/code/Magemonkeys/Saveinvoice/etc

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Event/etc/events.xsd">
  <event name="sales_order_invoice_save_after">
    <observer name="save_invoice_pdf" instance="MagemonkeysSaveinvoiceObserverSaveinvoice" />
  </event>
</config>

2. Create file Saveinvoice.php on app/code/Magemonkeys/Saveinvoice/Observer

<?php
namespace MagemonkeysSaveinvoiceObserver;

use MagentoFrameworkEventObserverInterface;

class Saveinvoice implements ObserverInterface
{
    protected $_pdfInvoiceModel;
    protected $_outputDirectory;
    private $_myPdfStorageSubDirectory = "pdfinvoices";

    public function __construct(
        MagentoSalesModelOrderPdfInvoice $pdfInvoiceModel,
        MagentoFrameworkFilesystem $filesystem
        ) {
            $this->_pdfInvoiceModel = $pdfInvoiceModel;
            $this->_outputDirectory = $filesystem->getDirectoryWrite(MagentoFrameworkAppFilesystemDirectoryList::VAR_DIR);
    }

    public function execute(MagentoFrameworkEventObserver $observer)
    {
        try{            
            $invoice = $observer->getEvent()->getInvoice();            
            $pdfContent = $this->_pdfInvoiceModel->getPdf([$invoice])->render();
            //save to file  var/pdfinvoices/[IncrementID].pdf
            $this->_outputDirectory->writeFile($this->_myPdfStorageSubDirectory. "/" . $invoice->getIncrementId() . ".pdf" ,$pdfContent);
        } catch (Exception $e){
            $message = $e->getMessage();
        }
        return $this;
    }
}