生成は可能です。
ただし、一般的なブラウザには保存はされません。
php
1<?php
2$value = 'something from somewhere';
3setcookie("TestCookie", $value);
4setcookie("TestCookie", $value, time()+3600); /* 有効期限は一時間です */
5setcookie("TestCookie", $value, time()+3600, "/~rasmus/", "example.com", 1);
HTTP/1.1 200 OK
Connection: keep-alive
Date: Tue, 14 May 2019 08:00:40 GMT
Server: Apache
Set-Cookie: TestCookie=something+from+somewhere
Set-Cookie: TestCookie=something+from+somewhere; expires=Tue, 14-May-2019 09:00:40 GMT; Max-Age=3600
Set-Cookie: TestCookie=something+from+somewhere; expires=Tue, 14-May-2019 09:00:40 GMT; Max-Age=3600; path=/~rasmus/; domain=example.com; secure
Content-Length: 0
Content-Type: text/html; charset=UTF-8
Via: 1.1 vegur