^ acts as a special character only at the beginning of the regular expression or subexpression (that is, after ( or |).
Reference: https://www.gnu.org/software/sed/manual/html_node/BRE-syntax.html
Examples
expr b : 'a\|^b'
expr ab : '\(^a\)b'