At noon on January 3, 2017, the terms of the current members of the Senate’s Class III will come to an end. At that point, the Senate consists of 66 sitting senators, 36 of whom caucus with the Democrats. If, before swearing in the new Senators, Vice President Biden recognizes the leader of the current majority, they can suspend the filibuster, call a vote, and approve the nomination of Merrick Garland.
This is procedurally sound. It's outside the normal order of business; but then, so was the Senate's refusal to vote on Garland, artificially preserving a Republican Supreme Court majority even though the Democrats have now won the popular vote in 6 of the last 7 presidential elections.
Donald Trump has demonstrated contempt for the constitution. We need a SCOTUS ready to stand up to him.