  We present the deepest constraints yet on the median rest-UV+optical SED of
$z\sim10$ galaxies, prior to JWST science operations. We constructed stacks
based on four robust $J_{125}$-dropouts, previously identified across the GOODS
fields. We used archival HST/WFC3 data and the full depth Spitzer/IRAC mosaics
from the GREATS program, the deepest coverage at $\sim3-5\mu$m to date. The
most remarkable feature of the SED is a blue IRAC $[3.6]-[4.5]=-0.18\pm0.25$
mag color. We also find a nearly flat $H_{160}-[3.6]=0.07\pm0.22$ mag color,
corresponding to a UV slope $\beta= -1.92\pm0.25$. This is consistent with
previous studies, and indicative of minimal dust absorption. The observed blue
IRAC color and SED fitting suggest that $z\sim10$ galaxies have very young (few
$\times10$ Myr) stellar populations, with $80\%$ of stars being formed in the
last $\lesssim 160$ Myr ($2\sigma$). While an exciting result, the
uncertainties on the SED are too large to allow us to place strong constraints
on the presence of a nebular continuum in $z\sim10$ galaxies (as might be
suggested by the blue $[3.6]-[4.5] < 0$ mag color). The resulting sSFR is
consistent with the specific accretion rate of dark matter halos, indicative of
a star-formation efficiency showing quite limited evolution at such early
epochs.
