  We present early time light curves of Type Ia supernovae observed in the
first six sectors of TESS data. Ten of these supernovae were discovered by
ASAS-SN, seven by ATLAS, six by ZTF, and one by \textit{Gaia}. For nine SNe
with sufficient dynamic range ($>$3.0 mag from detection to peak), we fit power
law models and search for signatures of companion stars. We find a diversity of
early time light curve shapes, although most of our sources are consistent with
fireball models where the flux increases $\propto t^2$. Three SN display a
flatter rise with flux $\propto t$. We do not find any evidence for additional
structure such as multiple power law components in the early rising light
curves. For assumptions about the SN properties and the observer viewing angle,
and further assuming that companion stars would be in Roche-lobe overflow, we
place limits on the radii of companions for six SNe with complete coverage of
the early time light curves. The upper limits are $\lesssim$\,32 R$_\odot$ for
these six supernovae, $\lesssim$\,20 R$_\odot$ for five of these six, and
$\lesssim$\,4 R$_\odot$ for two of these six. The small sample size does not
constrain occurrence rates of single degenerate Type Ia SN progenitors, but we
expect that TESS observed enough SNe in its primary mission (26 sectors) to
inform this measurement. We also show that TESS is capable of detecting
emission from a 1 \rsun\ companion for a Type Ia SN within 50 Mpc, and may do
so after about six years.
