There are student loans in virtually every country, including Europe, and I'd say they're quite commonly used. The difference is whether they're required to pay for tuition or not. For example, in Norway public universities (which are most, including the best ones) are tuition-free.
In countries like the Netherlands, there is tuition, but heavily subsidised. Fees are about 2k per year, and low (and partially to middle-income) households get a government stipend that is more than double that fee per year.
In short, people in these countries have to pay living expenses, tuition is pretty much covered. And a lot of these countries are quite small and have people living near the university, with decent public transportation, which is often free for students as well. As such lots of students live at home instead of on-campus, moving out for lifestyle reasons as soon as they can (often taking out loans to supplement a parttime job), rather than for the logistics of having to move to a place near the university.
In the US there's a lot of subsidies, state programs, scholarships etc as well. But many people still end up paying way more, especially if they're going out of state. And there's lots of people who end up having to move city to study somewhere, which means paying for room and board are very much a requisite part of their studies.
As such the loan amounts are nowhere near as large. Second, loans tend to be government issued, the cost-of-capital essentially tracking the interest on state bonds (e.g. treasury bills in the US) with a cap of 0%. This means in the Netherlands for example interest rates for student loans have been 0% for years and will likely remain at 0% for many years. This presents a wildly different outlook for students because borrowing $30k today isn't going to turn into having to pay back $100k over the course of the loan the coming decades, but just $30k, which is depreciating due to inflation in real terms over time.