Read David Swenson’s reply:
Having the students come to standing and then step forward is a good option. Without seeing the students in person, it’s difficult to give specific advice—but another possibility is to have them step forward as far as they can, then take one hand from the floor and place it on the knee to help them come up to standing. Then they can step the foot as far forward as is reasonable.
In addition, there are methods of Sun Salutation that do not require Downward-Facing Dog at all, and you could explore these options. Remember also that the breath should be an integral part of the practice. With proper breathing, their internal heat will increase, which will enhance the slow opening of the joints. Within the practice of Ashtanga, the breath and movement are woven together in a very precise manner. Every movement has a prescribed breath attached to it. As a general rule, whenever the body is expanding or lifting that action is attached to an inhale and exhales are applied whenever the body in lowering or contracting.
Stiffness in the hips and knees can take a long time to loosen, so my best recommendation is to instill patience and use the most appropriate alternatives you can to help your students keep moving.