Remember belief deals with different degrees of certainty, weal/strong belief etc.
I fail to see the relevancy. So what? Connect the dots.
Would you say you lack belief in that I have a dog if I told you I do?
Why would your lack of belief in something affect my observation of the fact that dogs exist? Connect the dots...
Do they need to know what my proposition was to not lack belief in it?
Not at all. Your lack of belief in dogs has nothing to do with me. I lack knowledge (gnosis) or your belief (pisteuo or pistis) status on dogs. You're attempting to conflate two things into the same thing and they aren't no amount of conflation attempts will change that.
Hence you need know what the proposition is to attribute a degree of belief to it.
Ah, I see the problem. You're ALSO conflating my knowledge of your status of belief with yours. I KNOW (not believe) that babies do NOT believe in god. Whether or not babies know any of this is irrelevant.
Read this slowly....you can't believe in something until you know about it, but you can absolutely lack belief in something whether or not you've ever heard of it. Whether or not I know anything about what you know or believe is irrelevant regarding that.