Domains of Dread certainly implies that it was the first domain. I found this tidbit on page 25 of the pdf:
"It has long been the tradition of scholars in Ravenloft to use the Barovian calendar when keeping track of events in the
Demiplane of Dread. This is done for many reasons, custom and practicality among them. The fact that it is the accepted
standard in Barovia, Necropolis, and among the wandering Vistani makes it as good a yardstick as any. This being the case,
we shall adopt the same practice here."
Edited to add: Domains of Dread says that Barovia was the first and only domain for the first 196 years of existence on the Demiplane of Dread until the Mists brought in Forlorn in the year 547.