If you did want an exactly even split, you could assign every even numbered student randomly and every odd numbered student to the opposite group of the studen

If you did want an exactly even split, you could assign every even numbered student randomly and every odd numbered student to the opposite group of the student before them. That guarantees an even split and doesn't require all the participants to be known in advance. It also guarantees that you split evenly any group of people arriving at similar times, so no correlation between arrival time and outcome will affect the study.