Get index of each capture in a JavaScript regex

I want to match a regex like /(a).(b)(c.)d/ with "aabccde", and get the following information back:

"a" at index = 0
"b" at index = 2
"cc" at index = 3

How can I do this? String.match returns list of matches and index of the start of the complete match, not index of every capture.

Edit: A test case which wouldn't work with plain indexOf

regex: /(a).(.)/
string: "aaa"
expected result: "a" at 0, "a" at 2

Note: The question is similar to Javascript Regex: How to find index of each subexpression?, but I cannot modify the regex to make every subexpression a capturing group.

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