I understand it is a theory used to try to explain the lack of transitional fossils.
Yes, and it has many adherents as well as detractors. Probably the best rendition of it is by Stephen Jay Gould in 'The Structure of Evolutionary Theory'. Certainly, I would suggest, there is a case to be made for it alongside the case for stasis and graduated evolution.
Tens of thousands of years is still an extremely short period in the evolutionary time scale. What I am saying is that the profound advance in the capabilities of the human mind was evidently not a gradual process in the evolution time line.
However, now you have at least accepted that we have evidence for creative abilites in certain hominids(not just homo sapiens) going back tens of thousands of years, then it is quite reasonable to surmise that such creative abilities did not necessarily start with the dating of first discoveries, but the driving force of that creativity might well have been illustrated in forms that have not survived(e.g. dance, sound, body painting). There is evidence, for instance, in South Africa of the selection of the deliberate production of ochre pigments which might, I stress, might have been used for body decoration. This was some 164000 years ago.
Another evolutionary trend in hominids, and, although you may not accept this as evidence of increasing 'consciously driven artistic abilities'( I assume you think they are a gift from God), does seem to have correlation to greater thinking power, greater social interaction(and, therefore, greater awareness) and possibly the sophistication of language. This evolutionary trait is the increase in brain size in hominids over millions of years. The cranial capacity of early hominids, such as aferensis annd africanus, was in the range of 500 cm3, and this gradually increased(habilis c700cm3), erectus(c900cm3) to homo sapiens( c1500 cm3). Compared with other mammals, the neocortex of primates has changed a great deal. In most mammals it accounts for 30-40% of the brain. in primates it is larger still and in humans it accounts for c80% of the brain mass. The neocortex is basically the thinking part of our brain and seems to have an important part in the development of language and social relationships.(see Robin Dunbar) Hence I would suggest that you are limiting your suggestions simply to homo sapiens. If you looked at the bigger picture then you just might just see the evolutionary trend towards the greater capabilities of the mind was a process which took millions of years.