We present AlInAsSb digital alloy staircase avalanche photodiodes (APDs) grown on GaSb substrates with low-noise behavior for near- to mid-infrared optical sensing applications. Detectors that rely on electron ionization, such as traditional APDs or photomultiplier tubes, suffer from non-deterministic gain, which manifests itself in the form of noise. In this work, we leverage the widely tunable AlInAsSb band parameters afforded by the digital alloy growth technique to design multi-step staircase APDs that incorporate deterministic spatial localization of impact ionization events. Using these methods, we demonstrate the first implementation of staircase APDs with deterministic 2 [superscript N] gain, extremely low excess noise (F(M) ~ 1.1), and linear noise power scaling with gain, unlike the quadratic relationship observed in conventional APD noise. We further explore the staircase APD design with electrostatic and Monte Carlo simulation analyses to study low-noise APD carrier dynamics, namely: thermionic emission, tunneling, and impact ionization. Furthermore, we use the knowledge gained from those parameterization studies to produce 4- and 5-step staircase APDs. Future work will focus on the pursuing higher step counts to reap the benefits of the low-noise, deterministic gain characteristics of the staircase APD architecture. Additional work will focus on wavelength-flexible staircase APDs for low-noise mid-IR sensing applications