We attach the invoices in the WooCommerce email notifications based on the order status. If you don’t have any option selected under WooCommerce > PDF Invoices > Documents > Invoice > Attach to, then the invoice won’t be created/attached.
You could check if you have any option selected there, if so, uncheck all the options, save the settings and try placing a test order, to measure the time the order placing takes.
If the order is placed faster, maybe your server have low resources, what would explain the fact of the slow performance of your site while processing the PDF generation. In such case, my recommendation is to contact your hosting provider, explaining the case, so they can help you further with this subject.
If you’re sure this is not something related with resources availability, I would recommend creating a staging site, disabling all the plugins, except WooCommerce and our plugin, and place an order to check if the same behavior happens. If the PDF is created faster, then start enabling one plugin at a time, repeating the test on every plugin activation, to try to determine which is the one that is slowing down the order placement process.
Could you please confirm that you ran the tests only having WooCommerce and our plugin? If you run the tests having other plugins activated, you won’t see an accurate result.