The hacking attempts against the company, whose board once included Joe Biden’s son, Hunter, began in early November.

It’s unclear what the hackers found, but the timing and scale of the attacks suggest a search for material that could embarrass the Bidens. Mr. Trump’s push for Ukraine to investigate the Bidens set off the chain of events that led to his impeachment.

Response: Joe Biden’s presidential campaign sought to cast the Russian effort as an indication of his political strength. Neither the Russian government nor Burisma responded to requests for comment.

Another angle: Senate Republicans indicated on Monday that they would not seek to summarily dismiss the impeachment charges against Mr. Trump, proceeding instead to a trial that could begin as soon as Wednesday.