According to this link, much of Earth's water is older than the Sun, which implies that Earth itself is older than the Sun. If this is the case, then what is the centre of the Solar System before the Sun was created? And where is "that centre of the Solar System" in present time?
According to this link, much of Earth's water is older than the Sun, which implies that Earth itself is older than the Sun.
There is something faulty in your logic. From your link:
In its youth, the Sun was surrounded by a protoplanetary disk, the so-called solar nebula, from which the planets were born. But it was unclear to researchers whether the ice in this disk originated from the Sun’s own parental interstellar molecular cloud, from which it was created, or whether this interstellar water had been destroyed and was re-formed by the chemical reactions taking place in the solar nebula.
A protosolar nebula would have a center of mass, which would remain the center of mass of the solar system if not too much external to it fell in over the aeons.
So the team created models that simulated a protoplanetary disk in which all the deuterium from space ice has already been eliminated by chemical processing, and the system has to start over “from scratch” at producing ice with deuterium in it during a million-year period. They did this in order to see if the system can reach the ratios of deuterium to hydrogen that are found in meteorite samples, Earth’s ocean water, and “time capsule” comets. They found that it could not do so, which told them that at least some of the water in our solar system has an origin in interstellar space and predates the birth of the Sun.
“Our findings show that a significant fraction of our solar system’s water, the most fundamental ingredient to fostering life, is older than the Sun, which indicates that abundant, organic-rich interstellar ices should probably be found in all young planetary systems,” Alexander said.
The "old" water could just be a huge water comet from interstellar space that fell on the earth while it was quite young, for example. Or maybe the whole solar system moved into a part of space that had a lot of space "water junk rocks". Or....
The present barycenter would not be too far away from the proto system barycenter, due to conservation laws.