They aren't trying to prove a negative, they are investigating a number of extremely serious crimes that may involve the president or members of his campaign/administration.
You seem really, really desperate to stop this investigation. Why? Wouldn't it make more sense to allow the professionals to decide what is worth investigating and what is not? They seem to think this is very, very worth investigating.
I've gone on record here with my doubts that the top levels of the Trump campaign colluded with the Russian government help them win the election. While I still believe that, I think there is substantial evidence of corruption and inappropriate or illegal contacts and meetings, and members of Trump's cabinet have already been caught in lies.
Under these circumstances, even some of the biggest Russia skeptics, like Glen Greenwald, are calling for a full and independent investigation, and I think it's pretty hard to make any serious case why one should not proceed.
I think the resistance to that investigation is probably because almost everyone recognizes that Trump is a corrupt man that surrounds himself with corrupt people, and any investigation is likely to turn up at least some of that corruption, more so than knowledge or suspicion of actual high level collusion with Russia, but that's just my speculation.