how to spend one night and one day without hotel in Madrid

The ONLY time to arrive is 12:00 am? Are you sure? Where are you getting you info?

There is a luggage-check at Puerta de Atocha Station, but I doubt that it is open 24 hours a day, so it may be of no help.

That's an 11-hour train trip you're talking about. I'd check skyscanner for flights. Multiple airlines have flights, some of them non-stop.

You can probably find an inexpensive place to stay. Expedia shows rates as low as $13/nite and a couple of dozen places below $25/nite. Just make sure the place accepts late night arrivals. Not an expert, but a hostel and a Spanish hostal are not the same.

Yes, Madrid is a late night city, but that means bars and nightclubs, not museums. And while you've probably heard about the late dinner hours, dinner starts at around 10 PM, so it's largely finished by midnight. So, there's no convenient place to be with a big suitcase at that hour.

I also agree that Madrid has very inexpensive accommodations, and that booking one is a good idea; just make sure you're clear with them that you will be arriving late, and make sure there will someone staffing the desk when you will be checking in (at less expensive places, the desk is usually not staffed all night).

And finally, I agree that you should look into flying, or taking a different train.

I too, would encourage you to seek an alternative.

No doubt you can find a flight a little more or less than this monotonous train ride

So was that a typo when your other post implied you were starting in Sevilla? Now it's Geneva? It's a long expensive train ride, and with a rail pass it's 2 or 3 more seat reservation fees. On my test date, the DB train schedule link shows 3 connection options with only 2 changes of train and one of those arrives at 23:10 instead of 00:02. If you're planning to visit Paris and/or Barcelona, you can make one or both stops along the way to break up this long travel route. Or you could fly.