  We study minimizers of non-autonomous functionals \begin{align*} \inf_u
\int_\Omega \varphi(x,|\nabla u|) \, dx \end{align*} when $\varphi$ has
generalized Orlicz growth. We consider the case where the upper growth rate of
$\varphi$ is unbounded and prove the Harnack inequality for minimizers. Our
technique is based on "truncating" the function $\varphi$ to approximate the
minimizer and Harnack estimates with uniform constants via a Bloch estimate for
the approximating minimizers.
