The intrinsic magnetic topological insulators MnBi$_2$X$_4$ (X = Se, Te) are promising candidates in realizing various novel topological states related to symmetry breaking by magnetic order. Although much progress had been made in MnBi$_2$Te$_4$, the study of MnBi$_2$Se$_4$ has been lacking due to the difficulty of material synthesis of the desired trigonal phase. Here, we report the synthesis of multilayer trigonal MnBi$_2$Se$_4$ with alternating-layer molecular beam epitaxy. Atomic-resolution scanning transmission electron microscopy (STEM) and scanning tunneling microscopy (STM) identify a well-ordered multilayer van der Waals (vdW) crystal with septuple-layer base units in agreement with the trigonal structure. Systematic thickness-dependent magnetometry studies illustrate the layered antiferromagnetic ordering as predicted by theory. Angle-resolved photoemission spectroscopy (ARPES) reveals the gapless Dirac-like surface state of MnBi$_2$Se$_4$, which demonstrates that MnBi$_2$Se$_4$ is a topological insulator above the magnetic ordering temperature. These systematic studies show that MnBi$_2$Se$_4$ is a promising candidate for exploring the rich topological phases of layered antiferromagnetic topological insulators.