The atomically thin MnBi₂Te₄ crystal is a novel magnetic topological insulator, exhibiting exotic quantum physics. In this work, using time-resolved optical techniques, we report a systematic investigation of coherent interlayer phonons, ultrafast (de)magnetization and coherent magnon dynamics in few-layer MnBi₂Te₄ as a function of layer number, temperature and applied magnetic field. Pronounced coherent phonon oscillations from the interlayer breathing mode are directly observed in the time domain and further confirmed by ultralow-frequency Raman spectroscopy measurements. Below the Neel temperature, we observe laser-induced (de)magnetization processes that can be used to accurately track the distinct magnetic states in different magnetic field regimes, including showing clear odd-even layer number effects. In addition, strongly field-dependent antiferromagnetic magnon modes with tens of gigahertz frequencies are optically generated and directly observed in the time domain. These measurements present the first comprehensive overview of ultrafast interlayer phonon and spin dynamics in this novel 2D antiferromagnet, paving the way for potential applications in 2D antiferromagnetic spintronics and magnonics as well as further studies of ultrafast control of both magnetization and topological quantum states.