Is it permissible to step back a little before prostrating in order to provide enough space to avoid colliding with the person in front of me?

Slight movement during prayer, if done out of necessity or for the prayer's benefit, is permissible and does not invalidate it. It is authentically reported that the Prophet, peace and blessings be upon him, carried Umamah [his granddaughter] while praying, and prayed on the minbar to teach the people, and opened the door while praying, and hurried to block a sheep that passed in front of him. If the movement is minimal, such as pushing away someone passing by, or taking off one's sandals, or adjusting one's cloak, it does not invalidate the prayer.