Once you have registered your NFZ account at ZUS, you should make your first payment. This way, your insurance will be valid/active that very same day.
Also, you need to submit a new DRA form at the ZUS office for every month you are paying your fees.
HOWEVER, you also CAN submit more than one DRA form at a time.
In sum – you can make just 1 visit to the bank [or post office] and 1 visit to the ZUS office and still take care of everything for the entire calendar year.