Zero inflated continuous outcome variables

I am trying to model a continuous outcome variable(non-integer, with excess zeros) by two independent variables.

I have seen that people have referred to the compound poisson gamma model( https://doi.org/10.1111/2041-210X.12122) as one of the possible models to deal with such a problem.

I’d like to get your opinion regarding to which statistical approach will you recommend solving this problem using R?