How could one know that Nibbana is the cessation of consciousness if there is no consciousness? How could one know that Nibbana is the cessation of consciousness if there is no consciousness?
I can't see how one could know.
Nibbana is experienced when the mind (including consciousness) is free of defilements. So, there is no permanent cessation of consciousness for the living arahant, unless you mean the cessation of defiled consciousness.
This is also known as Nibbana element with residue left or Unbinding property with fuel remaining, from Iti 44. The residue or fuel remaining refers to the undefiled aggregates including consciousness.
Ven. Thanissaro's commentary on Iti 44:

With fuel remaining (sa-upadisesa) and with no fuel remaining
(anupadisesa): The analogy here is to a fire. In the first case, the
flames are out, but the embers are still glowing. In the second, the
fire is so thoroughly out that the embers have grown cold. The &quot;fuel&quot;
here is the five aggregates. While the arahant is
still alive, he/she still experiences the five aggregates, but they do
not burn with the fires of passion, aversion, or delusion. When the
arahant passes away, there is no longer any experience of aggregates
here or anywhere else.

Or do you mean Nirodha Samapatti? In this state, the person entering Nirodha Samapatti would have temporary complete cessation of consciousness.

Nirodha Samapatti:
'attainment of extinction' (S. XIV, 11), also called
saññā-vedayita-nirodha, 'extinction of feeling and perception', is the
temporary suspension of all consciousness and mental activity,
following immediately upon the semi-conscious state called 'sphere of
neither-perception-nor-non-perception' (s. jhāna, 8).