Can we determine a security parameter in the hybrid argument where the number of hybrids is polynomially bounded but not known?
a function &quot;polynomially bounded&quot; means there exists $d\in \mathbb{N}$ such taht
$f(\lambda)\leq \lambda^d$ asymptotically.
You don't have to know $f$, but if you want to bound the advantage of your adversary asymptotically, you have to know a such $d$ which verifies this inequality.
If you don't, then you can't deduce anything. But in general, if you look the proof in details what is $n$, and why it has been claimed polynomially bounded, it's easy to find a such $d$, such that $n\leq \lambda^d$ asymptotically.