Within the single relaxation time approximation, the collision term in the Boltzmann equation is approximated as $$\Big(\frac{\partial f}{\partial t}\Big)_{\rm coll}=-\frac{(f-f_{\rm eq})}{\tau}$$ where $f\equiv f(\textbf{r},\textbf{v},t)$ is the distribution out of equilibrium and $f_{\rm eq}=f_{\rm eq}(\textbf{v})$ is the Maxwell-Boltzmann distribution, for example.
To show that at $t\to \infty$ the $f$ relaxes to $f_{\rm eq}$, one needs to specify the nonequilibrium distribution $f(\textbf{r},\textbf{v},t)$ at some initial time $t=t_0$. How does one specify that?