best NN architecture for point prediction
Since your outcome $y$ is restricted, you should check „beta regression“ in which the outcome is „squeezed“ into the interval $ \hat{y} \in [0, 1]$. See an example in R here: http://r-statistics.co/Beta-Regression-With-R.html

To my best knowledge, there is no "off the shelf" NN equivalent of beta regression.

You could of course use a "normal" NN for regression with dense layers with a sigmoid output layer. I.e. use a normal regression setup and change that last layer to have a sigmoid output (which is between 0,1). 

What could be interesting as well is a boosted beta regression: https://cran.r-project.org/web/packages/betaboost/betaboost.pdf

Beta regression is also available for GAM (generalised additive models), which are very flexible in handling non-linearities (https://stat.ethz.ch/R-manual/R-patched/library/mgcv/html/Beta.html). 

Ultimately, you need to check which approach works for you given your objectives and second order restrictions. It could (probably) also be okay to use a normal boosting approach (e.g. LightGBM or Catboost) - so without a beta link function. In this case some of the $\hat{y}$ could be $&gt;1$ or $&lt;0$. If you do not care too much about few "overshooting" predictions, you could also achieve good results with "normal" regression.