FLPrincessGrad

My partner is finishing up his PhD in neuroscience and he did not have a publication when he got accepted. 

I applied to top neuroscience programs this past semester, and most of the undergraduates who I interviewed with didn't have publications. It's the norm, not the exception.
 
That said, are you currently doing research yourself? Hard to tell what "volunteering in some labs" actually entails, but research experience is definitely necessary for a neuroscience PhD