Humans knew Earth is a sphere since at least the 3rd century B.C., far before the first spaceflight and before NASA was founded. Flat Earthers have no choice but to slander NASA to defend the flat-Earth belief, but there is no need to rely on NASA to know that Earth is a sphere.
If flat-Earthers desire to retain their belief in a flat-Earth, then need to invent elaborate “explanations” about why there are images of spherical Earth taken from space. It is the reason that NASA gets often mentioned in their arguments. They have no choice but to slander NASA and accuse it lying. To support their assertions, they invented various elaborate scenarios that they regard as “fact” with minimal evidence. Without believing in such scenarios, it is impossible for someone to believe in a flat-Earth.
On the other hand, spherical Earth is a fact that we can verify from simple observations everyone can do ourselves. There is no need to involve NASA to know Earth is a sphere. Humans from centuries ago managed to do that. And it is trivial for us living in the modern world to do that.
Flat-Earthers often get confused by the scenarios they invented themselves. The scenario that “NASA is lying” is fallaciously regarded as “proof” of a flat Earth, even though it is merely a prerequisite for them to believe in a flat Earth. The scenario can only be used as far as for dismissing information from NASA. When a simple observation that anyone can do themselves confirms spherical Earth, many flat Earthers will bring up NASA in the discussion. It is a standard logical error we often observe in the flat-Earth community.
On the other hand, because we know Earth is a sphere from personal observations, we can understand that NASA is not lying about the shape of the Earth. And this builds NASA’s reputation. We can also know for sure that various claims from flat-Earthers are wrong, and that made us think very hard before believing anything else that they claim.
Flat-Earthers invented various hoaxes to discredit NASA, so it would be possible for them to believe a flat-Earth. For the rest of us, addressing their slanders against NASA is merely a side activity; it is not required to prove that Earth is a sphere.