Application of the Adjoint Functor Theorem

Question

Let $F\colon \mathcal{C}\rightarrow\mathcal{D}$ a functor. Then, one obtains a functor $\tilde F\colon \textbf{Set}^\mathcal{D}\rightarrow \textbf{Set}^\mathcal{C}$ (composing with $F$). I want to show that $\tilde F$ has a left adjoint by using Freyd's Adjoint Functor Theorem. I have checked all the assumptions but the existence of a weakly initial set of objects in the comma category $(G\downarrow\tilde F)$, where $G$ is any functor $\mathcal{C}\rightarrow \textbf{Set}$. That's where I have the problem. I think I have to choose a set of the form $\{ ( \mathcal{D}( FA, -),\eta^{A})\ \mid A\in |\mathcal{C}| \}$, but I don't know how to choose the natural transformations $\eta^A$ (or maybe I should take coproduts of representable functors?). Can anyone give me a hint?