Legally speaking no, you’re not allowed site access to any construction site without a White Card. Construction comes with some hazards and that shiny white card proves you’ve carried out the training required to stay safe on a site.
However, you will have scheduled site visits with your site supervisor (who definitely has their White Card!).
You can also do as many site drive-bys as you want, but we don’t recommend getting out and going on site no matter how tempted you are. Especially when there are trades around. Your safety comes first!