It sounds like WGCNA is what you're looking for. I don't know of any good a priori minimum sample number, though I would worry that 3, particularly with no replicates, might be too few to be of use. I would think that the biological question you want to ask is, "Can the change in gene coexpression over the surveyed developmental timepoints be meaningfully modeled by recruitment/suppression of a limited number of gene modules, each presumably driven by different promoters or some other coordinated event?" You really need replicates to answer most of the more interesting questions in biology.

In my opinion the more the samples the better the network. You could try getting the correlation coefficient between the genes based on their expression across conditions and construct a network based on a cut-off (say 0.9). Other methods for eg., information theoretical approaches seem to work well with larger sample size.

For simple correlation based networks you need at least 8-10 samples to be able to build some sort of network.

So far the smallest networks accepted in literature using RNASeq data are those from Iancu (Mouse, 21 samples) and Giorgi (Arabidopsis, 65 samples)