Considering the amount of time that even a minimized Senate trial would require, it seems that even if the Senate started immediately, it’s not clear that they could remove Trump from office before January 20. And that’s presuming there are 67 votes to remove, which is still a tall order.
As Dan McLaughlin lays out in detail, Trump can still be impeached after he leaves office. Keep in mind, barring Trump from seeking the presidency again requires conviction by the Senate. Assuming all Democratic senators voted to convict, 17 of the 50 Republican senators would have to vote to convict to bar Trump from the presidency. That said, a vote to convict with less than 67 votes but more than a party-line vote would still represent a stain upon his already-dark record.
If Congress cannot impeach and remove the president quickly, they might as well investigate the matter thoroughly. The country would be well-served by a complete and detailed explanation of the president’s actions and inaction on January 6.