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The Laser Interferometer Space Antenna (LISA) mission is a space-borne observatory designed to detect and characterize gravitational wave sources inaccessible to ground-based detectors. The mission relies on laser interferometry to measure changes in space-time. In this context, non-avoidable noise sources within the LISA system, including tilt-to-length coupling, reduce the detector's resolution and complicate achieving the mission's goals unless appropriate mitigation strategies are implemented. This paper applies Time-Delay Interferometry Infinity (TDI-∞) for tilt-to-length noise estimation in LISA and assesses its suitability from the perspective of system identification and calibration for the first time. The recently published TDI-∞ concept indicates a different frequency response within the LISA measurement band compared to the standard methodology of TDI second-generation. Our main contribution is demonstrating the advantages of the TDI-∞ algorithm for tilt-to-length noise calibration in space-borne interferometer constellations. Specifically, we show that this algorithm improves the estimation performance of tilt-to-length noise due to its frequency behavior while requiring less computation time. The reduction in computational effort afforded by the TDI-∞ algorithm accelerates the availability of calibrated TDI data for astrophysical analysis if required by the LISA science community. The improvement in estimation performance underscores the concept's potential to enhance the detector's sensitivity further.