is there any reason you're specifically looking to not get sun protection? I've seen people request for SPF...or people like me who don't really care if it has it or not (my lotion has it anyway).
But "SPF" itself just stands for "Sun Protection Factor" which basically means you've put something to cover your skin to protect you from the UVB rays from the sun. Even a t-shirt has "SPF" technically, since having a t-shirt on will help protect you from getting burnt in the sun moreso than being naked in the sun. Things will advertise their levels of SPF because they know people want specific levels or higher levels. But I don't think I've heard of anything specifically advertising that it absolutely doesn't contain SPF (whether they advertise it or not).
I would think that almost anything you put on your skin that stays on your skin (doesn't get fully absorbed) will have a little bit of sun protection in it, just purely because you're putting something on your skin.
edit: I just noticed you also specifically listed titanium dioxide. Might be more reasonable to look for makeup that doesn't have titanium dioxide than "zero spf" since...I don't know if that's even possible technically. There are a variety of ingredients that are used in makeup, it'll be easier to find one that's missing a single ingredient than it is to be missing a general opaqueness factor to the sun. Good luck on this though, I use mineral foundations which generally do have titanium dioxide in them, so I'm unfamiliar with the ingredients in other brands.