Do you know a good reference for the existence and uniqueness of a smooth structure on $3$-manifolds?
As far as I understand topological $3$-manifolds admit a unique smooth structure. I could find the following references for this result:
It follows from Hauptvermutung for $3$-manifolds (Theorems 3 and 4 in ) and from the fact that a combinatorial $3$-manifold has a unique smoothing (see Theorem 4.2 in ).
However, I am not quite satisfied with this answer since it requires a good understanding of what is written in these papers. For someone like me, who does not know geometric topology well, it would be better to have a reference to an explicit statement.
 M. W. Hirsch, B. Mazur, Smoothings of piecewise linear manifolds. Annals of Mathematics Studies, No. 80. Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974.
 E. E. Moise, Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermutung. Ann. of Math. 56 (1952), 96-114.
There is a related post, but I do not find the answer posted there satisfactory. Smooth structures on closed $3$-manifolds are unique up to diffeomorphism? I think Moise does not talk about smooth structures only about triangulations.