  The Universe is currently undergoing accelerated expansion driven by dark
energy. Dark energy's essential nature remains mysterious: one means of
revealing it is by measuring the Universe's size at different redshifts. This
may be done using the Baryon Acoustic Oscillation (BAO) feature, a standard
ruler in the galaxy 2-Point Correlation Function (2PCF). In order to measure
the distance scale, one dilates and contracts a template for the 2PCF in a
fiducial cosmology, using a scaling factor $\alpha$. The standard method for
finding the best-fit $\alpha$ is to compute the likelihood over a grid of
roughly 100 values of it. This approach is slow; in this work, we propose a
significantly faster way. Our method writes the 2PCF as a polynomial in
$\alpha$ by Taylor-expanding it about $\alpha = 1$, exploiting that we know the
fiducial cosmology sufficiently well that $\alpha$ is within a few percent of
unity. The likelihood resulting from this expansion may then be analytically
solved for the best-fit $\alpha$. Our method is 48-85$\times$ faster than a
directly comparable approach in which we numerically minimize $\alpha$, and
$\sim$$12,000 \times$ faster than the standard iterative method. Our work will
be highly enabling for upcoming large-scale structure redshift surveys such as
that by Dark Energy Spectroscopic Instrument (DESI).
