Training a Variational Autoencoder (VAE) for Random Number Generation

I have a complicated 20-dimensional multi-modal distribution and consider training a VAE to learn an approximation of it using 2000 samples. But particularly, with the aim to subsequently generate pseudo-random numbers behaving according to the distribution. However, my problems are the following:

1. Is my approach fundamentally or logically flawed? Specifically, because unlike image data, the random numbers are of geometric nature and thus take negative values and could also be considered noisy.
2. How do I find the right architecture aside from simple trial and error? Obviously, I do not necessarily need 2D-Convolutions. But instead, 1D-Convolutions could be considered a good choice to capture the correlations. I'm also not sure on how I properly decide on the number of hidden layers and nodes.