Seems like Shakespeare was not always wealthy. Historical information points at the moment of his father's death as the moment when Shakespeare actually inherited the father's coat of arms, which immediately gave him a title of "gentleman", in a time when actors (which he was one) and drama people were considered from the lower classes.
With this new title, he began to write plays. Another indication of his wealth is his home in Stratford Upon Avon. It is described as "the biggest house" in the lot. He called it "New Place". Also, the Shakespeare historical society mentions that he was a big land owner, and bough more than a hundred acres in a time when the poor were going through dire straits.