A Federal District Court judge in Washington declined to bar associates of Elon Musk from gaining access to the Education Department’s data systems, finding that the University of California Student Association, which sued to block the incursion, had not shown that students were irreparably harmed in the process.

In a late order on Monday, Judge Randolph D. Moss wrote that lawyers representing the students had failed to show that sensitive student data from the department’s databases had been illegally disseminated in a way that would justify an emergency restraining order barring Mr. Musk’s team from the agency’s systems.

Judge Moss described potential harms to the students as “entirely conjectural.” He added that the lawsuit “provides no evidence, beyond sheer speculation, that would allow the court to infer” that the Education Department or Mr. Musk’s team would “misuse or further disseminate this information.”

Lawyers representing the students had asked the court to temporarily bar Mr. Musk’s team from sifting through databases that contain identifying information about students and their families, which lawyers behind the lawsuit said had already occurred in violation of the Privacy Act of 1974.

During a hearing on Friday, Judge Moss seemed to grow annoyed about the lack of clarity that the government could provide about Mr. Musk’s Department of Government Efficiency operatives and their roles.

The office, which is not an official department but a small team housed within the executive office of the president, has already appeared to have driven the Education Department to slash funding for education research and proposed killing federal contracts by introducing new A.I.-driven tools.