As Buddha is mentioned in the Bhagavatam does it prove that it was written after the time of Buddha?

From: ANIL V UMESH

In Srimad Bhagavatam Lord Buddha is mentioned as one of the Avataras of Lord Krishna. Atheists took this as an opportunity to point out that mentioning  of Lord Buddha in the holy scripture  clearly establish that Srimad Bhagavatam was written not during Bhagwan Vyasa’s time five thousand years ago but later during A.D ie. medieval times. Please  clear the doubt.