There is a possibility to login to the instance via the URL. You just pass you login name and password via URL paremeters like follows:
https://{INSTANCE_NAME}.service-now.com/login.do?user_name={USER_NAME}&sys_action=sysverb_login&user_password={PASSWORD}
Just replace marked placeholders with your real data and you are good to go. But note: of course, this is a very unsecure way of logging in.