Let's at least be realistic. No ex-president is being impeached, it can't be done. Trump has ALREADY been impeached (actually maybe not until the articles are delivered to the Senate). That was the big rush here, they had to get it done before 1/20. The trial portion can happen whenever, but the "fun" is that once the Senate starts it they are supposed to ONLY work that, so they can't work Biden's agenda.
The house portion is SUPPOSED to be a hearing, it wasn't, the Senate, has 2 options:
1) Dismiss out of hand because the House "evidence" says nothing happened
2) Hold their own hearing
They can, but probably won't, simply look at the evidence supplied by the house, and essentially throw it out.