How can we efficiently derive ANY inverse solution of a single convolutional layer?

Question

Given a single convolutional layer h and its output y, how can one find any x' that satisfies h(x')=y efficiently?

e.g. x->(conv2d)->y, where x∈R^{3*64*64}, y∈R^{64*32*32}, and conv2d: Conv2d(3,16,kernel_size=(3,3),stride=(2,2),padding=(1,1),bias=False)

• I understand that the forward pass of a convolutional layer is a N-to-1 mapping, hence it is not invertible, however, I wish to find ANY solution for the task.
• Unlike deconv, or transposed conv layers, I wish to find the EXACT solution x that produces y.