Here's a short demo on this:
% A is your 3D array
A = rand(4,4,4);
A(:,:,2) = nan; % making second layer nan for demonstration
% Check if a layer contains only NaN
layersWithNaN = all(all(isnan(A), 1), 2);
% 1. Get the list of layers containing only NaN
listOfLayersWithNaN = find(layersWithNaN);
% 2. Get the array where the layers containing only NaN have been removed
A(:,:,listOfLayersWithNaN) = [];
