I mean, sure, you can model a simple linear regression fitted via Least Squares (pretty much what they did 200 years ago) with a one hidden layer feed-fwd Neural Network, but the theorical framework for NNs is quite different.
For Least Squares, you do not even use a hidden layer. Just a single dense layer from input directly to output. You also do not use an activation function (or use the identity activation function). That is, everything that makes neural networks special.