Is there any way to put the Google Tag manager Identification code into the child theme?

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You have a couple of options –

  1. Install a plugin that adds GTM for you. This makes it very easy, but it does add another plugin to the site. Site Kit supposedly slows down a site more than you would expect.

  2. Make a copy of header.php and put it in your child theme folder. Now you can make edits to this file without the edits being overwritten when the parent theme is updated. That’s how the child theme works. Anything you want to edit gets copied into the child theme. By default you only get the stylesheet and functions.php, but you can put any theme file into the child theme for editing.