Contact Form 7 to featured image

Thanks @Judd Franklin for the directions. I was also missing $submission->uploaded_files();.

Here is the working code for those who are looking for the same answer:

function image_form_to_featured_image( $contact_form ) {

    $submission = WPCF7_Submission::get_instance();
    $posted_data = $submission->get_posted_data();

    // Creating a new post with contact form values
    $args = array(
        'post_type' => 'projects',
        'post_status'=> 'draft',
        'post_title'=> wp_strip_all_tags( $posted_data['title'] ),
        'post_content'=> wp_strip_all_tags( $posted_data['pitch'] ),
    );
    $post_id = wp_insert_post($args);

    // Retrieving and inserting uploaded image as featured image
    $uploadedFiles = $submission->uploaded_files();

    if( isset($posted_data['featured']) ){
        $featuredUpload = wp_upload_bits($posted_data['featured'], null, file_get_contents($uploadedFiles['featured']));


        require_once(ABSPATH . 'wp-admin/includes/admin.php');
        $filename = $featuredUpload['file'];
        $attachment = array(
            'post_mime_type' => $featuredUpload['type'],
            'post_parent' => $post_id,
            'post_title' => sanitize_file_name($filename),
            'post_content' => '',
            'post_status' => 'inherit'
        );

        $attachment_id = wp_insert_attachment( $attachment, $filename, $post_id );

        if (!is_wp_error($attachment_id)) {
            require_once(ABSPATH . 'wp-admin/includes/image.php');
            $attachment_data = wp_generate_attachment_metadata( $attachment_id, $filename );
            wp_update_attachment_metadata( $attachment_id,  $attachment_data );
            set_post_thumbnail( $post_id, $attachment_id );
        }
    }
}
add_action( 'wpcf7_before_send_mail', 'image_form_to_featured_image' );