The broadest generalization is that, whatever is systematically lacking in your language, that thing is hard to do. If your language has no [ʁ], it is hard for you to produce [ʁ]. If words do not begin with [nd, mb, ŋg], it is hard for you to product such clusters. Hence English speakers would have problems pronouncing [ŋgata], [ŋko], but most Bantu-language speakers have no problem pronouncing that. Some Bantu-language speakers have problems with [ŋko] but not [ŋgata] because in some languages, nasal plus voiceless consonant clusters don't exist, but parallel clusters with voiced stops do.
The primary reason why Modern English doesn't have initial clusters like [zb] is that Middle English didn't have then, which is because Old English didn't have then, which is because proto-Germanic didn't, as far back as the eye can see. A few people have nativized [zb] clusters, owing to a period of exposure for a couple of years to the name Zbigniew Brzezinski, but otherwise there has been no source of such clusters being added to English. North Saami, on the other hand, adopted [sp,st,sk] clusters from neighboring Germanic, because the level of contact between Saami and Germanic was much higher than the level of contact between English and Polish.
A challenging and unanswered empirical question is whether there is a specific significant disadvantage to initial [zb] clusters. If a language doesn't have consonant clusters, doesn't have /z/ or doesn't have /b/, then it is not going to have initial [zb] clusters. Once you narrow the survey down to languages with /z, b/ and with initial clusters, then you can start surveying frequency of language with no restriction against [zb] versus languages with such a restriction. Some Arabic dialects have such clusters, historically arising from /zibV.../, /zubV.../ (similar to how such clusters arose in Slavic). To even determine that there is a significant trend against [zb] (one that isn't just a function of limits on /z,b/ or clusters), you would need a broad survey of the facts, which we don't have.
I applaud the effort to consider an acoustic explanation, since people frequently attribute perceptual problems to articulatory causes: in this case, I think the explanation behind *[zb] is more physical (aerodynamic). The aerodynamic challenge of [z] is that to produce turbulence, you need rapid air flow, and to produce voicing, you need rapid airflow, so [zb] in any position is quite challenged. In initial position it is particularly challenged because airflow has to rise very quickly from zero, but then because of the stop, it will be extinguished soon. Thus initial [zb] is more susceptible to phonetic modifications, compared to [zm]. The prediction is that [zb] should be more likely to be missing compared to [zm]. Systematic statistics on this question across the world's languages are lacking.
