I suspect that journal editors could be reluctant to seek out early-career scientists as peer reviewers (see M. Casado Nature 560, 307; 2018). Researchers at this stage are often invisible to editors, because they have no publications or online research profile. Senior scientists, who have the grounding and scope necessary for in-depth peer review, are seen as a safer bet. In my experience, however, training graduate students in the critical assessment of research papers goes a long way towards equipping them for the task.
I ask graduate students participating in a research-methods course to independently review the same selection of manuscripts before these are submitted for publication. They then collectively discuss the merits or inadequacies of each paper. In the process, the students learn how peer review works, how to avoid pitfalls in publishing and how to prepare and improve their own papers.
Ultimately, such group peer-teaching exercises could help to improve the peer-review process for all researchers, even the experienced ones.
Nature 561, 177 (2018)