  We prove two separate lower bounds -- one for nondegenerate convex domains
and the other for nondegenerate $\mathbb{C}$-convex (but not necessarily
convex) domains -- for the squeezing function that hold true for all domains in
$\mathbb{C}^n$, for a fixed $n\geq 2$, of the stated class. We provide explicit
expressions in terms of $n$ for these estimates.
