Snyder had said he wanted to honor the Starman mythology, but in a way that didn't invalidate what James Robinson did with Jack Knight in the 90s. But the presence of the cosmic staff immediately raises questions, as does the fact that the JSA are forgotten still, aren't they?
The fact that Stargirl was already shown to exist in this continuity and had Jack's cosmic staff seemingly independent of him already muddies the water significantly.