Based on it's orbit, it almost certainly came from outside our Solar System.
NASA is less than 60 years old. The science and equipment for measuring these phenomena is even younger.
There are known objects orbiting our Sun with orbits spanning hundreds of years.
The question of how it is known that this asteroid is interstellar is a fair one. It has not been answered, and it needs to be answered, else we are not talking about rigorous science here, we are instead talking tabloid science. The PR people of NASA often do that to create interest in the field. The photo they released is an ‘artist’s conception’ and their write-up may also be an ‘artist’s conception’.
“While originally classified as a comet, observations from ESO and elsewhere revealed no signs of cometary activity ... “
The quote is telling, the astronomers are not sure what they have.
Every object that is ‘slingshotted’ past our Sun immediately draws a curved trajectory because of the constant yet decreasing forces of the Sun’s gravitational fields. It is possible that an object attains a distance and speed sufficient to exit our Solar System, but the NASA write-up mentions variation in speed which is likely why it was classified as a comet.
No one is saying the astronomers who are touting this are wrong. But they need to explain and defend their assertions because that is what science is, a debate based on measurable, testable, repeatable, replicable quantifications.
“Almost certainly” is not direct evidence. If a bullet is buried in a tree we can calculate were it “May Have” come from, but a photo of the shooter would be “Direct Evidence”. In other words there may have been a prior collision that set it on it’s current course.
Cheers,