My understanding is you wish to display just the posts table portion of the posts admin panel on a frontend page?
If so, there is not a template tag or function you can call to easily do this. Your page template will need to generate the table on it’s own. You could start by examining how the admin panel table is generated in wp-admin/edit.php. Unfortunately, it uses private methods. Your code could extend the class WP_List_Table to do something similar. Or you could just start from the beginning and create your own table structure.
You’ll also need to figure out the CSS, but if you can crate the table structure, this will be trivial.