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Which native method I can use to publish the WordPress custom post type post programmatically

You can use wp_insert_post to insert and publish the WordPress custom post type post programmatically

$post_id = wp_insert_post(array (
    'post_type' => 'post_type',
    'post_title' => $title,
    'post_content' => $content,
    'post_status' => 'publish',
    'comment_status' => 'closed',  
    'ping_status' => 'closed',  
));