The hacking attempts against Burisma, the Ukrainian gas company on whose board Hunter Biden served, began in early November, as talk of the Bidens, Ukraine and impeachment was dominating the news in the United States.

It is not yet clear what the hackers found, or precisely what they were searching for. But the experts say the timing and scale of the attacks suggest that the Russians could be searching for potentially embarrassing material on the Bidens — the same kind of information that Mr. Trump wanted from Ukraine when he pressed for an investigation of the Bidens and Burisma, setting off a chain of events that led to his impeachment.

The Russian tactics are strikingly similar to what American intelligence agencies say was Russia’s hacking of emails from Hillary Clinton’s campaign chairman and the Democratic National Committee during the 2016 presidential campaign. In that case, once they had the emails, the Russians used trolls to spread and spin the material, and built an echo chamber to widen its effect.