Was Sauron's war on Gondor in the 2nd Age a mistake?

After the destruction of Numenor Sauron returned to Mordor and quickly launched a suprise attack on Gondor trying to destroy the newly established kingdom before it would become too powerful. In my mind this was a great mistake, because not only did he fail to do so, he also alerted evyerone that he had survived, whereas previously at least the Numenorians thought he was gone for good, and most crucially, this attack on Gondor caused the good guys to team up and form the Last Alliance.