That doesn't say that covid is a variant of influenza and towards the end of the July it was believed that aprox 20% of New York City residents had already been infected with covid.

https://www.mountsinai.org/about/newsroom/2020/study-finds-1... It's a discussion of a study published in nature last November.

Despite this cases rose very sharply between October and early January. Your theory doesn't comport with reality as observed.