After creating your header, you can assign it globally to all pages at once:
1. From the WordPress left menu, go to Appearance > Customize.
2. From the Customizer left dashboard, click on Header.
3. For the Header Type, select Custom and select your header Template below.
4. Click on Close and Publish the changes.
Note: You can use Default Header but it has limited settings and styles rather than the header that you create with Elementor.
If you want to assign custom header to a specific page only, please refer to this article.