Hello
Thank you for your query.
There is a way you can try. You can go to Template Options -> Layout builder, then you have to add a new section in the top. In that section, you have to put a module.
You have to create that module from the Module section. The module would be of SP Page builder type and after creating it, you can edit with SP Page builder and add social icons as per your choice with the Page builder addon.
Also from the Module settings, you need to set a position for this module and use this position in the section that was created in the beginning from Layout builder.
Please check the screenshots below:
You can let me know if that helps. Also, you will need to use some custom css as well to make it appear the way you want to.