You may doubt there is enough time to impeach Trump by the 20th.
There is plenty of time for the House to vote a bill of Impeachment. There is not enough time for the Senate to try him and convict him by the 20th.
BUT, Speaker Pelosi can send the bill of Impeachment to the Senate at her leisure, long after Trump is no longer President.
Impeached doesn’t mean convicted. The action of the House is the Impeachment. If McConnell’s Senate could ratify a SCOTUS nominee in a day, the House can impeach in a day