how to make a new page affected by a theme’s index.php layout?

WordPress loads templates in order from most specific to least specific, depending on which templates files exists.

For instance, lets say we have a wordpress page by name of “Audio Collection” with page ID of 14. WordPress would look for files by these names in order, and return the template for the first file name it checks that exists in your active theme.

• page-audio-collection.php
• page-14.php
• page.php
• index.php

So if you wanted to, you could create a duplicate of index.php, and call it page-audio-collection.php, and modify it as needed. That template would only be loaded when viewing the Audio Collection page, and all other pages would continue loading their current template file.

You could also create and assign a Custom Page Template, which would override all of the normal template hierarchy I outlined above.

read more at WordPress Template Hierarchy