In order to be eligible to begin university studies in the US, you must have completed full-time education in your native country. So, in the UK, this is up to the age of 18 and usually means completing and passing A-Levels and/or BTEC or IB courses. For Danish students, this would be age 19 once you graduate from Gymnasium.
For most four-year universities, you have up to a maximum of one gap year to use before you’re considered to old to enrol as a student-athlete (so you’d be 19 years old by this point, or 20 if you’re Danish!)