Hi Olivia, it sounds like your device is incapable of ultra-low latency operation. Unless the noise to cancel is steady-state and exclusively tonal, the total latency time of the system has to be faster than the speed of sound between the error microphone and the loudspeaker.
The example here uses the Speedgoat since its latency can be as low as approximately 2 samples. If you intend to develop ANC for something physically small like headphones, you will need that ultra-low latency (and probably increase the sample rate of the model to further reduce latency).
So you could add buffering to the error microphone in the model to make it execute, but the ANC performance will be severly limited if the latency is too long.