They can, just not right away. An Assistant Prof. in Philadelphia I had interviewed with for a postdoc position told me that since his lab is new, the school wo

They can, just not right away. An Assistant Prof. in Philadelphia I had interviewed with for a postdoc position told me that since his lab is new, the school won't let him recruit PhD students for the first year. He can take postdocs and trainees, though. I think there's also a practical problem in attracting students to a new lab. Another Assistant Prof I'd interviewed with at a premier research institute in New York had established her lab over 3 years ago, and still hadn't managed to recruit either a PhD student or any postdocs. She may be an outlier, of course.