Any Way To Find An iPhone That Isn't Signed Into iCloud?
The only way would be the old-fashioned - go look for it, ask others if they've seen it, etc.

You don't specify what you mean by "signing into the phone" except that it is not iCloud, you've signed into. If the service you did sign into (for example Facebook Messenger?) does have some kind of location tracking, it might give you a last known position.

If you have just misplaced the phone, you can't really report it as stolen with Apple to get it blocked on cell networks.