DIFF = PL = TOP for surfaces (earliest references)

Question

I am looking for the original references that show that there is essentially a unique PL and smooth structure on a topological manifold of dimension 2.

Radó ("Ueber den Begriff der Riemannschen Flache" 1925) for the existence and Kerékjártó ("Voriesullgen iiber Topologie", 1923) for the uniqueness show together that PL=TOP. This can be found in the celebrated book by Kirby–Siebenmann "Foundational Essays on Topological Manifolds, Smoothings and Triangulations".
For DIFF = PL , this expository paper by Milnor points that the result follows from work from the '60s-'70s for manifolds of dimension $n<7$ (later references appear in this upvoted post from MO). However I think that this might be a overkill to show DIFF = PL for surfaces. Is not there really an earlier argument?

At the end of the day I am really interested in the fact that DIFF=TOP for surfaces. Hatcher in his The Kirby torus trick for surfaces says that

The first proof that surfaces can be triangulated (and hence smoothed) is generally attributed to Radó in 1925.

Does the "hence smoothed" mean that DIFF=TOP for surfaces was already known in the 20s after Radó's work? If so, how does it follow?

See the 1960 Munkres reference I gave here. I do not know an earlier one. [Smoothing a triangulated surface is easy, but approximating a PL homeomorphism by diffeomorphisms requires more work.] — Moishe Kohan, Nov 16 '22 at 20:43
Could you elaborate on how to put a smooth structure in a triangulated surface, please? — Minkowski, Nov 16 '22 at 21:42
Do you know how to extends diffeomorphisms of the unit circle to those of the unit disk? — Moishe Kohan, Nov 16 '22 at 22:42
I do, but I genuinely do not see how this helps. At any rate I read in your linked answer that this would prove existence but not uniqueness of the smooth structure, is that right? — Minkowski, Nov 17 '22 at 10:13
The link proves the harder result, the uniqueness. With a bit more thought, you realize that one can deduce the existence from the same proof as well. But you have to read the paper (JSTOR is free). — Moishe Kohan, Nov 17 '22 at 12:06

DIFF = PL = TOP for surfaces (earliest references)

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