Except that as a sibling comment mentions; that generalizes to any size of group - for six players you could roll one d6, and have "that" player go first.
But apparently the constraints are: every player rolls one die once.
> But apparently the constraints are: every player rolls one die once.
That doesn't eliminate the natural scheme, it just adds some useless die rolls. You can have each of two players flip a coin and choose player A when player A flips heads or player B when player A flips tails.
Useless depends on context here; I believe the idea is that each player gets a feeling of agency (they go in the order dictated by "their" luck, not leaving the decision to someone elses roll).
The most pragmatic would probably be to shuffle N cards from ace(one) through N - and let everyone draw).
But apparently the constraints are: every player rolls one die once.