Unlike some other roles in advertising, becoming a copywriter does tend to require some specific skill development before starting in an agency (but there are always exceptions to the rule).
Copywriters may have a tertiary degree in fields such as English or Languages, Fine Arts, or Creative Communications. Increasingly, this might also include study of digital design or technology.
Copywriters and Art Directors often get their first jobs in advertising by developing a 'book'. This is a portfolio of advertising ideas you have created. These don't have to be real ads that have appeared in the world. They are speculative - how you would advertise products and brands that you've chosen.
A 'book' allows a creative director to see how you think, get a sense of the quality of your creative thinking. It's how they probably got their first job as a creative.