The basic problem is that gamma only has support on x \in (0, \infty) so your likelihood isn’t going to be able to accommodate observed values of zero. Your intercept is very likely negative (mean=1, but SD=10), which could (depending on the values of your predictors and coefficients) yield negative (i.e., invalid) means for your likelihood.
As I stated here, outcomes that are counts are commonly modeled as Poisson, ZIP, and negative binomial.