Causality of linear time-invariant systems inherently defines the wave-matter interaction process in wave physics. This principle imposes strict constraints on the interfacial response of materials on various physical platforms. A typical consequence is that a delicate balance has to be struck between the conflicting bandwidth and geometric thickness when constructing a medium with desired impedance, which makes it challenging to realize broadband impedance modulation with compact structures. In pursuit of improvement, the over-damped recipe and the reduced excessive response recipe are creatively presented in this work. As a proof-of-concept demonstration, we construct a metamaterial with intensive mode density that supports strong non-locality over a frequency band from 320 Hz to 6400 Hz. Under the guidelines of the over-damped recipe and the reduced excessive response recipe, the metamaterial realizes impedance matching to air and exhibits broadband near-perfect absorption without evident impedance oscillation and absorption dips in the working frequency band. We further present a dual-functional design capable of frequency-selective absorption and reflection by concentrating the resonance modes in three frequency bands. Our research reveals the significance of over-damped recipe and the strong non-local effect in broadband impedance modulation, which may open up avenues for constructing efficient artificial impedance boundaries for energy absorption and other wave manipulation.