The Los Angeles Times of May 1, 1934, introduced the season’s San Francisco Seals like this:
Chief interest in the Seals will be centered on the arrival here of “The Great” Mails, who admits being an attraction in himself, and “Dead Pan” DiMaggio, the sensational young slugger. Mails does all the talking for the club while DiMaggio does most of the hitting. They say DiMaggio is bigger and better this year. He grew more than an inch and added fifteen pounds to his frame during the winter and the Seals are getting ready to play a $100,000 price tag on him. In case you have forgotten, Joe is the lad who hit safely in sixty-one consecutive games for a world’s record last season. But hitting isn’t his only virtue. DiMaggio also fields superbly and throws with the best of them.
The above is one example of how DiMaggio’s fame had spread beyond the Bay Area with that 1933 hitting streak: in his late teens he was, it seems to me, a phenom comparable to Bryce Harper and Lebron James.
In March 1935, the Times reported that he had arrived in Los Angeles for an examination of his knee after tearing it in May 1934, as required by the New York Yankees as part of their purchase of him from the Seals. DiMaggio was holding out with the Seals, but the Times said Yankees scout Bill Essick convinced him to get the examination.
DiMaggio stayed with the Seals for 1935, with the Yankees biding their time while they waited to see if his knee would hold up for the duration of a season. On May 5, 1935, the Times said:
When Vince came back the following spring  he asked the Seals if he could bring out his young brother, Joe, for a tryout. Joe, he said, was a shortstop. The Seals said yes, so Joe got his chance. But Joe as a shortstop was one of the wildest throwers ever seen, but he could hit, so the Seals switched him to the outfield also. And then what did Joe do but run his brother right out of a job.
Both Joe and Vince were raised in San Francisco, where their father is a fisherman. As as the two boys were 13 years of ago their dad put them to work on his fishing smack. And pulling in those heavy seines gave each of them the powerful wrists and arms that make it so easy for them to “poosh ‘em oop” out of the park.
I recently read Richard Ben Cramer’s Joe DiMaggio: The Hero’s Life. According to Cramer, the Times was right about Joe being an erratic shortstop and good hitter, wrong about the tryout story, and terribly wrong about the seines story. Vince was only a reluctant fisherman, who preferred selling newspapers and being in the city, and left home before he was 18 to play professional baseball. Joe’s mother, Rosalie, then refused to have husband Giuseppe force Joe into the fishing business after he’d dropped out of school at 14 or 15, and Joe instead sold newspapers, then was playing a kind of semipro ball by the time he was 16. He was good enough to be known as a coming star by the summer of 1932, making it inevitable that the Seals would try to get him on the team.