JASMINE GAO, who is 19, just wasn’t the classroom type. So instead of languishing in college, she dropped out after her freshman year.

Ms. Gao decided that she didn’t want to continue studying at Baruch College, part of the City University of New York. At first she considered transferring to Carnegie Mellon in Pittsburgh, but she changed her mind when she saw that her tuition bill would be around $44,000 a year, with only a small amount of financial aid available. “I didn’t want to come out of college with $200,000 in debt and have to spend 10 years paying it off,” she said.

Yet she still sought a way to nurture her interest in technology. A year later, Ms. Gao holds the title of data strategist at Bitly, the URL-shortening service based in New York.

How did she catapult from dropping out of college to landing a plum job? She became an apprentice to Hilary Mason, chief data scientist at Bitly, through a new two-year program called Enstitute. It teaches skills in fields like information technology, computer programming and app building via on-the-job experience. Enstitute seeks to challenge the conventional wisdom that top professional jobs always require a bachelor’s degree — at least for a small group of the young, digital elite.