Low-resolution infrared spectroscopy from JWST confirms the presence of SiC and likely metallic iron dust around asymptotic giant branch (AGB) stars in the Sextans A dwarf galaxy, which has a metallicity  ∼ 1%–7% Z _⊙ . While metal-poor carbon-rich AGB stars are known to produce copious amounts of amorphous carbon dust owing to the dredge up of newly synthesized carbon, this is the first time that Si- and Fe-bearing dust has been detected at this extreme metallicity. Of the six AGB stars observed, one is an intermediate-mass ( ∼ 1.2 – 4 M _⊙ ) carbon star showing SiC dust, and another is an oxygen-rich M-type star with mass  ∼ 4 – 5 M _⊙ that is likely undergoing hot bottom burning. The infrared excess of the M-type star is strong, but featureless. We tested multiple dust species, and found that it is best fit with metallic iron dust. Assuming its dust-production rate stays constant over the final 2–3 × 10⁴ yr of its evolution, this star will produce  ∼ 0.9 – 3.7 times the iron dust mass predicted by models, with the range depending on the adopted stellar mass. The implications for dust production in high-redshift galaxies are potentially significant, especially regarding the assumed dust species used in dust evolution models and the timescale of AGB dust formation. Stars on the upper end of the AGB mass range can begin producing dust as early as 30 – 50 Myr after they form, and they may therefore rival dust production by supernovae at high redshift.