cpt and page sharing same base permalink

No,it is not possible. The reason behind this is that, the child page with the parent slug which is same as the cpt slug will be behaved as the cpt post and wp will search for that post rather than looking for the child page with same parent slug.
And if you try the parent page, it will be replaced with the cpt archive page.
This is based on the template hierarchy and how the WordPress handles the url for cpt, posts and pages.

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