Because of how Inertia works, simply using a return back() from you Controller after storing the new record, would cause the data list to be updated without refreshing the page.
public function index()
{
$posts = auth()->user()->posts();
// Render index page which also includes create form
return Inertia::render('Posts/Index', [
'posts' => $posts,
]);
}
public function store(Request $request)
{
// Some validation
$post = auth()->user()->posts()->create([
// Whatever fields
]);
return back(); // Back to index page. All this happens without refreshing
}