There's evidence that Star has been stopping time before, which is why Jotaro can use it nearly from the moment he becomes aware of the concept.
First it was in the prison, when Jotaro kept "magically" getting stuff from his "evil spirit". Star could only get it from the immediate vicinity, and since nobody saw items floating over to Jotaro, that means it happened in stopped time.
The second time that hints at this ability was during the poker game. The older D'arby seemed to know about The World's ability, and once he saw Jotaro getting a drink out of nowhere he must have realized that's the same (or similar) power, which meant Jotaro could have swapped all of his cards for good ones, and revealing The World's ability to him was extra dangerous.
Also, there's Jotaro's attitude towards his Stand. Whenever a problem arises he's like "my Stand can do it". Like when he removed the flesh buds, or made Star draw that fly, he just accepts that his Stand can do anything. And as we see from DIO's flashback, in order for this ability to work, it is important to believe that it will work.