  We bootstrap ${\cal N}=(1,0)$ superconformal field theories in six
dimensions, by analyzing the four-point function of flavor current multiplets.
Assuming $E_8$ flavor group, we present universal bounds on the central charge
$C_T$ and the flavor central charge $C_J$. Based on the numerical data, we
conjecture that the rank-one E-string theory saturates the universal lower
bound on $C_J$, and numerically determine the spectrum of long multiplets in
the rank-one E-string theory. We comment on the possibility of solving the
higher-rank E-string theories by bootstrap and thereby probing M-theory on
AdS${}_7\times{\rm S}^4$/$\mathbb{Z}_2$.
