Again if Obama was President the admin would have known this from the jump and then Obama would have pressed China letting them know they have a pandemic on their hands and they need to put out a statement saying so..
This study hasn't been peer reviewed and doesn't proof China knew about the new Virus in October. Most sources agree that they've started to notice the increase of strange pneumonia in November, the same time Trump got briefed by Intelligence Agency about it, if China realized about the new disease earlier Trump would've been briefed about it earlier.
Delay between emergence of a virus and it's detection isn't rare. Remember, the first Covid case might've reached US in December and some Coli posters also claim they suffer symptoms during December-January period but it took US CDC until February to detect their first case. This is despite US having the foreknowledge about the virus since, while China have no idea about the virus when they first encounter it.
While China deserve criticism for the delay between detection of the virus in December to release of genetic data and quarantine of Wuhan in January, there's no proof they know about the virus earlier than December.
Also the theory that the Virus might've spread earlier is not new.