cut one's teeth

cut one's teeth on sth (to get one's first experience in a particular job by doing something) — делать первые шаги, приобретать первый опыт ( в какой либо области)

cut one's political/professional, etc. teeth on sth (to get one's first experience of the type mentioned) — делать первые шаги, приобретать первый опыт (на политическом / профессиональном / др. поприще)

...actors who cut their teeth on low-budget films

The Prime Minister cut her political teeth on student debates.

Related vocabulary:
[делать первые шаги]