The Steyr company was first called, in 1864, "Waffenfabrik Josef und Franz Werndl & Comp.". It later became a joint stock company in 1869 and then became known as "Oesterreichische Waffenfabriks-Gesellschaft". This is what appears abbreviated on your receiver. In 1927 the name of the firm changed to "Steyr-Werke A. G.". So it is unlikely to have been made later than that, (though it would have taken a little while to use up parts inventory). This information comes from the companies' centenary publication (1864-1964), which was given to me when I visited the works at Steyr.

The double-headed eagle proof mark is Austrian, as we'd expect.

The proof mark "Not English make" was used between 1925 and 1955 according to A History of Proof Marks; Gun Proof in England in Gun Digest 1977. The absence of this mark means either that, (1) your gun was imported to England outside this period or, (2) it was never imported to England. However the mark V with a crown to me looks like a London "View" proof mark used between 1637 and 1955. So I'd say it did get imported to the UK at some point. I don't know of any similar Austrian proof mark this could be confused with, (see 1959 Gun Digest; "Development of proof in Austria-Hungary" and also Wirnsberger/Steindler Standard Directory of Proof Marks).

The 9,5x57 M.Sch. was released to the public in 1910. The company changed its' name in 1927. This is the approximate window that your rifle was made. What Lonewulf has said sounds perfectly plausible, about the T inside a circle. So that being the case, the rifle was made between 1920 (T-circle mark introduction), and 1927, (company name change). If it did get imported into the UK, (View-crown mark), but is not marked "Not English make", then it must have been before 1925. So that refines it to 1920-1925.

I think I read somewhere on this forum the year that "Made in Austria" was added to the front receiver ring, above where it says "Mannlicher-Schoenauer". I know they hadn't done so in 1920, but it was in use by 1925. There there's further confirmation.

So it's 35+ years older than 1960!