TIME Commissioning Observations: I. Mapping Dust and Molecular Gas in the Sgr A Molecular Cloud Complex at the Galactic Center

We present the processing of an observation of Sagittarius A (Sgr A) with the Tomographic Ionized-carbon Mapping Experiment (TIME), part of the 2021-2022 commissioning run to verify TIME's hyperspectral imaging capabilities for future line-intensity mapping. Using an observation of Jupiter to calibrate detector gains and pointing offsets, we process the Sgr A observation in a purpose-built pipeline that removes correlated noise through common-mode subtraction with correlation-weighted scaling, and uses map-domain principal component analysis to identify further systematic errors. The resulting frequency-resolved maps recover strong 12CO(2-1) and 13CO(2-1) emission, and a continuum component whose spectral index discriminates free-free emission in the circumnuclear disk (CND) versus thermal dust emission in the 20 km s$^{-1}$ and 50 km s$^{-1}$ molecular clouds. Broadband continuum flux comparisons with the Bolocam Galactic Plane Survey (BGPS) show agreement to within $\sim$5% in high-SNR molecular clouds in the Sgr A region. From the CO line detections, we estimate a molecular hydrogen mass of between $5.4 \times 10^5 M_\odot$ and $5.7 \times 10^5 M_\odot$, consistent with prior studies. These results demonstrate TIME's ability to recover both continuum and spectral-line signals in complex Galactic fields, validating its readiness for upcoming extragalactic CO and [C II] surveys.