The ATLAS experiment relies on real-time hadronic jet reconstruction and b-tagging to record fully hadronic events containing b-jets. These algorithms require track reconstruction, which is computationally expensive and could overwhelm the high-level-trigger farm, even at the reduced event rate that passes the ATLAS first stage hardware-based trigger. In LHC Run 3, ATLAS has mitigated these computational demands by introducing a fast neural-network-based b-tagger, which acts as a low-precision filter using input from hadronic jets and tracks. It runs after a hardware trigger and before the remaining high-level-trigger reconstruction. This design relies on the negligible cost of neural-network inference as compared to track reconstruction, and the cost reduction from limiting tracking to specific regions of the detector. In the case of Standard Model HH → bb̄bb̄, a key signature relying on b-jet triggers, the filter lowers the input rate to the remaining high-level trigger by a factor of five at the small cost of reducing the overall signal efficiency by roughly 2%.