Characterizing standard building materials such as concrete is challenging primarily because of the broad range of constituent component sizes within the material itself. Concrete, the most ubiquitous building material, contains critical components that span at least three orders of magnitude of physical size. This work introduces a nondestructive sequential impact test to extract transient nonlinear vibration behaviors that provide statistically significant holistic characterization of a heterogeneous building material, neat cement paste, on a centimeter scale sample. The sensitivity of the single impact vibration combined with the repeatability of the new sequential apparatus enables the extraction of statistically distinct transient nonlinear (slow dynamic) material memory behaviors. Experimental results on neat cement paste prisms and borosilicate glass blocks across several environmental states and damage conditions reveal an underlying phenomenon of transient nonlinear behaviors. Material damage and moisture state significantly affect the proper interpretation of the transient nonlinear material behaviors. The presented testing procedure and observations, supported by historical experiments, confirm that sequential impact reports a consistent transient nonlinear vibration behavior, and the measured behavior can identify damaged heterogeneous building materials.