+1 That was also my rule of thumb. But here @UGFan said to this Purchases made through these links may earn this site a commission from the eBay Partner Networkwatch that it has a 1945 case... May be a Sala's owner chimes in.
I too always thought that the 1950's was the earliest and always figured that the round waterproof pushers would have ushered the flat pushers out pretty quickly. It was seeing the occasional reference to WW2 vintage with the round pushers that had me wonder.
When I posted this I wasn't thinking about some of the earlier chronos, like the German pilots watches, ie. Tutima which had the round pushers. I do believe it is about the ability to protect better against water with the round pushers and "O" rings which will make an adequate seal.
Are we talking specifically UG or in general in chronographs? If in general in chronographs the 2 earliest chronographs I can think of that had round pushers are the (first) Mido Multichrono, extremely rare and dating more or less from 1935/1936 and the Gallet (as well as many other brands) with the clamshell case, dating from more or less 1937. If speaking specifically about UG I am not 100% sure but I think you can already find some round pushers already at the end of 30 (or at the latest very beginning of the 40s). The first UG Tri-Compax with round pushers instead I am sure dates from beginning of the 50s and had the small pushers ("spillini" in Italian). I think flat and round pushers coexisted a LONG time, at the end of the day even today many chronographs have flat pushers. I believe the reason is 2-fold: firstly, especially back in the day, a price reason, waterproof cases with round pushers were much more expensive than the other type and not everyone needed it so it made sense to also offer a cheaper but still very good version without round pushers. Also, I believe there is an aesthetic reason: even though now people tend to prefer round pushers as they look more sporty and contemporary, probably for the very same reason back in the day gentleman buying the watch as a luxury item as oppose to as a tool might have preferred the classier look of a chronograph with flat pushers.