Apparatus and associated methods relate to a time-interleaved integrating sampling front-end circuit using integrating buffers. In an illustrative example, a circuit may include N sampling layers of circuits, an ith sampling layer of circuits of the N sampling layers of circuits may include: (a) Xi buffers configured to receive an analog signal, Xi≥1, and, (b) Yi track-and-hold circuits, each track-and-hold circuit of the Yi track-and-hold circuits is coupled to an output of a corresponding buffer of the X buffers, Yi≥1, at least one buffer of the Xi buffers may include an integrating buffer, N≥i≥1. By implementing integrating buffers, a faster linear type of step settling response may be obtained as opposed to a slower exponential type of settling response.