It happened OTL. Sort of.
After Austro - Hungary began to collapse in autumn 1918, Vienna de facto lost control over the territories of the monarchy - Czechoslovaki and Hungary proclaimed independence, Croatia, Slovenia and Bosnia split proclaiming intent to join Yugoslavia and Galicia split as well, proclaiming its intent to join Poland - but refused to join the Kingdom of Poland and didn't join up until November same year. So technically an independent Galician state existed for a few weeks in september and october 1918.
You could have a PoD there, with Galicia refusing to join Poland for longer due to its government disagreeing with Warsaw - say, have the Nationalists take power in Poland, Galicia refusing to join, holds elections won by Socialists, proclaims independence or a socialist Republic. Whether it could last against the Ukrainians for long is a different matter, but you could have the independent and non-recognized Galicia to form and last longer.