Manually Editing header.php
You can add a Divi Builder layout to the header of your pages by editing the header.php file in Divi (or better yet, in a copy of the header.php file placed in a child theme).
To do so, replace this line in header.php:
<div id="page-container"<?php echo $page_container_style; ?>>
With these lines:
<div id="page-container"<?php echo $page_container_style; ?>> <?php echo do_shortcode('[et_pb_section global_module="5944"][/et_pb_section]'); ?>
The global_module="5944" part specifies the internal WordPress id of the global module ("5944" in this case). You'll need to change this to the id that WordPress assigns to your global module, as it will likely be a different value. To find this id, go to "Divi > Divi Library". This will take you into the Divi Library, which is where all the saved global modules (and other modules / layouts) are stored. You'll see a list of "layouts" and should hopefully be able to locate the name you gave to the global module you wish to use. Click on that global module to go to its edit screen. Here you'll see a simplified version of the Divi Builder which includes your global module. To get the id for your module you can now simply look up at address bar of the current browser tab. In the URL you should see a part that says"post=" followed by a number. This number is the id you need.
Note that if you have edited the Divi files directly, then your changes will be written by future updates to Divi and will need to be re-applied. This should not happen if you edited a copy of header.php in your child theme, but note that changes Divi makes to its own header.php file won't be transferred across to your child theme header.php and so you'd need to manually repeat your steps if you want to take advantage of any enhancements Divi makes to its own header.php file.
Using a Plugin
There are a couple of plugins for Divi which allow you to add Divi Builder layouts across your sites, in various places such as above and below the main header. These are:
The main advantage over these plugins, apart from being easier to use and requiring no coding, is that they should not be affected by Divi updates.