Dynamic tag management has never shown signs of negatively affecting page load time or execution speed. However, because dynamic tag management can be used as a delivery system (a way to deliver JavaScript, HTML, images, or other Web content), if you load a large file, or a large image at the wrong point during render time, you can slow down page load speed and increase code execution time on that page. If you lazy load images, and if you use asynchronous (non-sequential) scripts as much as possible, and you follow best practices regarding the code you add into dynamic tag management, you should not see negative performance impacts.
The Embed code should be hard-coded in the <head> section of your templates. This is a synchronous JavaScript include. The dynamic tag management engine is designed to work in a modular way, so scripts that do not apply to a particular page, site section, or domain will not load or execute when they are not needed. Most users increase the use of asynchronous (non-sequential) methods when deploying third-party scripts. This generally improves the perceived page load speed for site visitors. While the dynamic tag management main library file itself is loaded synchronously, most clients load any code from within dynamic tag management using the built-in asynchronous methods.
Please see below link for more info -
https://marketing.adobe.com/resources/help/en_US/dtm/wp_page_load_speed.html
