I could figure out how to execute a script from the terminal using the specific environment of the project.

At the NewProject directory:

...NewProject$ julia --project my_first_plot.jl

Or outside NewProject:

$ julia --project=~/path/to/NewProject/ ./NewProject/my_first_plot.jl

With --project, julia could use the information at the Manifest.toml where the version and packages were added.

At the end, I realized that the Manifest.toml has a similar purpose of a Python directory where the packages of a virtual environment are stored. This link helped me to know the difference.