= Solution
An empty universe with $\Lambda=0$ has $\Omega_{r,0}=\Omega_{m,0}=\Omega_{\Lambda,0}=0$. The present <Friedmann equation> then requires $\Omega_{k,0}=1$, so
$$
\boxed{H(z)=H_0(1+z).}
$$
The <Friedmann acceleration equation> gives $\ddot a=0$, hence $a\propto t$ after choosing its zero at $t=0$, and
$$
\boxed{q_0=0.}
$$
This is the <Milne universe>. A larger past <Hubble parameter> does not require negative $\ddot a$: even constant $\dot a$ produces $H=\dot a/a=1/t$. Equivalently, <deceleration parameter from the Hubble derivative> gives $q=-1-\dot H/H^2=-1+1=0$. The age is $t_0=H_0^{-1}$.
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