The LUX-ZEPLIN experiment recently reported limits on WIMP-nucleus interactions from its initial science run, down to $9.2\times10^{-48}$ cm$^2$ for the spin-independent interaction of a 36 GeV/c$^2$ WIMP at 90% confidence level. In this paper, we present a comprehensive analysis of the backgrounds important for this result and for other upcoming physics analyses, including neutrinoless double-beta decay searches and effective field theory interpretations of LUX-ZEPLIN data. We confirm that the in-situ determinations of bulk and fixed radioactive backgrounds are consistent with expectations from the ex-situ assays. The observed background rate after WIMP search criteria were applied was $(6.3±0.5)\times10^{-5}$ events/keV$_{ee}$/kg/day in the low-energy region, approximately 60 times lower than the equivalent rate reported by the LUX experiment.