Getting $frac{2pi}{hbar}$ factor in Fermi's Golden Rule without using limit of no time dependence

Fermi’s golden rule is: $$R = frac{2pi}{hbar} |langle f| Delta H_0 |i rangle|^2 rho(E)$$ and it looks like all derivations of this at some point use the limit of a time dependent perturbation becoming essentially time constant. My question is, if we assume a time constant perturbation from the start, how can we get this $frac{2pi}{hbar}$ factor since it should be consistent?