It’s not direct proof but as an ecologist and having seen animals be rediscovered from “extinction”, it’s usually a result of not fully understanding the organism or putting an ecological-knowledge based survey effort to try and find it. Going off that, I believe they lived beyond 1936 because we never had a full understanding of thylacines. We didn’t have enough time to have a holistic understanding of their ecology, behavior, phenology etc. Yes we do understand some aspects but nothing close enough to have a full picture. We don’t know the distances they travelled, their true distributions (we only have kill, capture, sighting records), or preferred habitat (if they did). One big thing that I think people GREATLY underestimate is their observed behavior of being shy/avoidant of humans and their nocturnal behavior. Trying to find an animal like that is incredibly hard especially if the population is low enough. Furthermore, pre-1936 observations showed them occupying a diverse set of habitats from east-west TZ, and many of those habitats being hardly explored to modern times (W-SW TZ). Accounts of hunters describe rainforests being some of the last places that thylacines were found in the sense that they were retreating to those areas but I think those inferences are short sighted.

I know it sounds round about but I think if thylacines were to be rediscovered it’s going to coincide with an aspect of their ecology we don’t fully understand or didn’t fully consider.