Therefore, it seems it doesn't work like this in Poland, does it?
T-Mobile do a starter pack for 25zł (2GB). They might work differently but you still only have a month to use the 2GB. However, some money might remain in credit on the account which you perhaps can then buy a top up or phone calls with. I am not at all sure, so you will need to ask at one of their shops in shopping malls etc. You will of course need an unlocked dongle-modem.