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The typical way to do something like this _without_ involving recursion would be to build an array and iterate through that.

However, in this case, recursion is a more appropriate option. With tree structures like HTML where you don't know ahead of time the depth or breadth of the tree, recursion is usually the easiest way to handle it because it's concise, readable, and efficient. (In terms of time complexity, you're looking at O(n) for recursion vs usually at least O(2n) and worst case O(n^2) or more for loop iteration.)

If you're concerned about stack size, you don't need to be. Most modern browsers have stack limits in the tens of thousands, and you're only adding one stack frame per child level of the HTML tree. If you have a HTML structure that's tens of thousands of levels deep, you have bigger problems!