Identifying the triangular-lattice compound YbZnGaO$_4$ as a spin glass

YbMgGaO$_4$ with the triangular-lattice structure has been reported to be a promising quantum-spin-liquid candidate. However, here we provide compelling evidence that its sister compound YbZnGaO$_4$ is a spin glass. We show that the spin-glass phase can give rise to all of our experimental observations, including no long-range magnetic order, prominent broad excitation continua, and absence of magnetic thermal conductivity. More crucially, from the ultralow-temperature a.c. susceptibility measurements, we unambiguously observe frequency-dependent peaks around 0.1 K, indicating the spin-glass ground state. We consider disorder and frustration to be the main driving force for this phase.