Second, we don't actually know how fast the fleet got from the Expanse to Earth. Consider that the Enterprise had to get from the Romulan Neutral Zone to Earth in the same amount of time. That should be several days' travel at least. Despite how the film was edited, it's reasonable to assume that the battle near Earth was a separate battle taking place days after the first engagement in the Expanse -- or else that it was a running battle lasting for days.
I thought Data said it would take either a few minutes or hours to get to the fleet during the briefing scene.
From context, he was saying it would take them 3 hours, 25 minutes to reach the Typhon Sector from their current location. Although it's true that Picard ordered a course set for Earth when the battle was engaged, which does imply it was close to Earth.
And note that he did say "Typhon Sector," not "Typhon Expanse." Maybe those are two different locations. After all, Typhon is a name from Greek mythology, and humans love drawing on classical mythology to name things in space. Heck, there's a real-life trans-Neptunian object by that name, 42355 Typhon, discovered in 2002. So the Typhon Sector could be much closer to Earth than the Typhon Expanse.
Although it's still problematical if the movie is claiming that the Romulan Neutral Zone is mere hours from Earth, even at maximum warp for the E-E.