  The tip of the red giant branch (TRGB) allows for the measurement of precise
and accurate distances to nearby galaxies, based on the brightest ascent of
low-mass red giant branch stars before they undergo the helium flash. With the
advent of JWST, there is great promise to utilize the technique to measure
galaxy distances out to at least 50 Mpc, significantly further than HST's reach
of 20 Mpc. However, with any standard candle, it is first necessary to provide
an absolute reference. Here we use Cycle 1 data to provide an absolute
calibration in the F090W filter. F090W is most similar to the F814W filter
commonly used for TRGB measurements with HST, which had been adopted by the
community due to minimal dependence from the underlying metallicities and ages
of stars. The imaging we use was taken in the outskirts of NGC 4258, which has
a direct geometrical distance measurement from the Keplerian motion of its
water megamaser. Utilizing several measurement techniques, we find
$M_{TRGB}^{F090W}$ = -4.362 $\pm$ 0.033 (stat) $\pm$ 0.045 (sys) mag (Vega) for
the metal-poor TRGB. We also perform measurements of the TRGB in two Type Ia
supernova hosts, NGC 1559, and NGC 5584. We find good agreement between our
TRGB distances and previous distance determinations to these galaxies from
Cepheids ($\Delta$ = 0.01 $\pm$ 0.06 mag), with these differences being too
small to explain the Hubble tension ($\sim$0.17 mag). As a final bonus, we
showcase the serendipitous discovery of a faint dwarf galaxy near NGC 5584.
