Do you count the Xiongnu and their predecessors as Scythians? There's some evidence that both were related and Iranic tribes, not to mention that the "Scythian" label itself is almost certainly applied way too broadly to a wide range of nomadic peoples and cultures . Also inherent in your question is the assumption that "Scythian" nomads
didn't push into China; given the paucity of sources from pre-Qin times it's not impossible to say that they didn't, and new genetic studies are just starting to lift the veil on who was living there and how they relate to modern Chinese. Interestingly, Scythian-related groups seem to have been in Xinjiang in the time period.
www.science.org
The Eastern Eurasian Steppe was home to historic empires of nomadic pastoralists, including the Xiongnu and the Mongols. However, little is known abou…
www.sciencedirect.com
Anyway, to get back to what seems to be the meat of your question, I think some sort of big nomadic influx into China is plausible at basically any point in its history. Interactions with the steppe are recorded as far back as the Han dynasty, and the last nomadic conquest was by the Qing. On the steppe side you need some sort of push/pull factors to make the nomads conquer or migrate into the region, things like climate change, population pressure, or conquerors, can provide the push, and grazeland and extracting sedentary wealth are typical pulls. It's not hard to imagine some sort of Scythian proto-Ghenghis Khan forming a tribal confederation that conquers the Persian Empire and then goes East into China themselves, or pushes other "Scythian" groups into the Han heartland in processes analogous to the Barbarian invasions of Rome or Turkish invasions of the Middle East.
The farther back you go the bigger the impacts naturally, pre-Qin in particular there's probably much more opportunity to disrupt the nascent Han civilization, and certainly pre-Zhou. Then you start running up into the question of geographic determinism; the Yellow-Yangtze river system do make a nice contiguous region for a unitary state to emerge, but I think there's room for multiple ones to exist in China, particularly more steppe-oriented northern and Western states and Southern states if the Han never really make it South of the Yangtze. Post-Qin however it's far more likely for natives to adopt Han culture and governments; the universal state ideology is already there, and the institutions that it set up are far too attractive for conquerors to use to put themselves on top of the entire region.
It goes without saying that a world without a mostly-united Han China would be very different from OTL. A more politically and culturally fragmented East Asia would likely be less stable and prosperous, significantly changing trade patterns throughout the region to India. Who knows what new ideologies or technologies might emerge from such a ferment, or how they could bounce back to the West. With a weaker, more steppe-focused "chinese civilization(s)" the maritime cultures in Japan, Korea, and Vietnam probably are more geopolitically active and strong, which maybe kicks off some sort of proto-colonialist SE Asian drive into Polynesia and India. Or maybe the main division becomes between the coastal and inland regions of China instead of North and South as OTL. Trite as it may be to say, the possibilities are endless.