Where did you try to make the reservation?
At the Czech Railway there are many trains available on that date.
The cheapest place to book is at the Czech Railway
https://www.cd.cz/en/spojeni-a-jizdenka/#hledej
NO these trains are not full. In PL f.e. REserv only open 30 days advance. Trains are not planes-also in this respect and to confuse all those from over the long oceans.
You probably stay the odd day in beautiful golden city Praha? Then simply take a few more min after arr in this old station HN now shopping centre to find the foreign desk and do it. In same hall is also a desk for DPP=the local tram+bus to buy that 24 hr ticket for urban transit. That was the way that was self-evident in times many young peopl travelled on Inter/EU-rails.
BTW-if you are collecting capitals visited-skip WAW-Krakow is THE touristy city in Pl to visit-far more interesting (even though I passed by WAW a few days ago)
NO these trains are not full. In PL f.e. REserv only open 30 days advance. Trains are not planes-also in this respect and to confuse all those from over the long oceans.
International trains to Poland can generally be booked 60 days in advance, but trains from 12 June have not been opened for booking yet.
Just try again later.