Regex to find variants of "Google"
Honestly there's not much code to comment on, it's also a programming challenge, so there's not much incentive to make it any better than it is. I too would have done it your way.

The only objective criticism I have is I'd just add a function regex_options to build the non-capturing group.

Other than that I'd apply this to the creation of g, o, l and e. As I think it's a little cleaner. But you may want to perform it before "".join, and after regex = (g, o, o, g, l, e).

import re


def regex_options(options):
    options = (re.escape(o) for o in options)
    return "(?:{})".format("|".join(options))


g = regex_options(["g", "G"])
o = regex_options(["o", "O", "0", "()", "[]", "&lt;&gt;"])
l = regex_options(["l", "L", "I"])
e = regex_options(["e", "E", "3"])

regex = "^{}$".format("".join((g, o, o, g, l, e)))

print(bool(re.match(regex, input())))


If this were professional code, I'd suggest using an if __name__ == '__main__': block, and possibly a main function.