Šutej was born in Ljubljana and began competing in athletics at an early age, practising in a variety of events from the age of seven. A change of coach at her local club saw the arrival of a pole vault specialist, who encouraged her to focus on vaulting the high bar. She made her international debut at the 2005 World Youth Championships in Athletics and finished eighth in the pole vault final. Her first medal came the following year as she was the runner-up behind Zhou Yang with a Slovenian junior record mark of 4.25 m.