There are some event-driven fast trades still done by humans, like after news or responding to economic releases, but hedge funds have highly-educated people modeling the effects of an interest rate change or earnings release as their full-time job. This area is also becoming dominated by bots doing sentiment analysis.
I think the retail trader could have an edge in a few ways. One would be an illegal edge like inside information or market manipulation. Another would be finding illiquid stocks that proprietary traders and hedge funds won't bother with and trading using similar techniques. You could also look for extreme situations that model-based traders can't understand well due to lack of data, like a merger target breaking away. Those trades would be very risky though.
FWIW I'm a professional trader and never day trade my own account or pick individual stocks. My company allows it, but I don't believe I have any edge in doing so. I just buy and hold a portfolio of ETFs.