Very difficult to answer given the information provided but you probably want …
'has_archive' => false,
'rewrite' => array('slug'=>"https://wordpress.stackexchange.com/",'with_front'=>false),
… as part of your arguments when you register the post type and then you can add the post type to the main query for that home/front page…
function add_cpt_to_home($qry) {
if (is_front_page() || is_home()) {
$post_type = (array)$qry->get('post_type');
$post_type[] = 'post';
$post_type[] = 'project';
$post_type = array_unique(array_filter($post_type));
$qry->set('post_type',$post_type);
}
}
add_action('pre_get_posts','add_cpt_to_home');
Or write a secondary query to pull that post_type.
$args = array(
'post_type' => 'project'
);
$projects = new WP_Query($args);
if ($projects->have_posts()) {
while ($projects->have_posts()) {
$projects->the_post();
the_title(); // etc
}
}
Not tested very well, but as I said it is hard to answer given the information provided.