Mr Kennedy was selected by hundreds of party members to be the Liberal candidate in an upcoming by-election in the southern Sydney seat, triggered by the resignation of former prime minister Scott Morrison.
Mr Kennedy beat Sutherland Shire Mayor Carmelo Pesce and war widow Gwen Cherne for the pre-selection for the safe Liberal electorate.
"It was very humbling to be chosen by the group of 300 locals," he told reporters on Tuesday.
"I'm here to listen (to the community) and stand up to this Labor cost of living crisis, to hold the Labor government and Anthony Albanese to account."
There had been calls for the Liberal Party following their 2022 election defeat to pre-select more female candidates for winnable seats.
Mr Kennedy said there was already 50-50 representation for southern Sydney seats, with Jenny Ware representing the Liberals in the neighbouring electorate of Hughes.
"I haven't heard that issue (of female representation) raised by anyone I've met over the time I've been here, the last time I've been in politics," he told Sky News.
"What I'm hearing now is cost of living, that is issue one, two and three."
Mr Morrison also brushed off concerns about representation, saying the pre-selection process was carried through.
Scott Morrison has brushed off concerns about female representation in the Liberal Party. (Dan Himbrechts/AAP PHOTOS)
"These are decisions that party members make, and we respect those," he told reporters.
"What matters is in a political party, the party members get to have their say, and they've had their say, and there was a very strong win for Simon."
But Victorian MP Keith Wolahan said his party needed more women, particularly in the House of Representatives.
"What we have to do is to feed through members and pre-selection candidates who will then succeed, and there are so many talented women in the party who are doing that, who are putting their hands up now," he told ABC's Q and A program on Monday night.
Mr Kennedy is a partner of consulting firm Banksia after leaving McKinsey, according to his LinkedIn profile.
He contested John Howard's former seat of Bennelong at the 2022 federal election but came up short against Labor's Jerome Laxale after an almost eight per cent swing against the Liberals.
Cook is a safe Liberal seat, with the party holding it by a more than 12 per cent margin, with 55 per cent of the primary vote.
While Mr Kennedy lives outside of the Cook electorate, he said he would move to the area with his family on Friday.
A date for the by-election has yet to be set.
Labor is yet to determine whether it will formally run a candidate in Cook.
Prime Minister Anthony Albanese said Cook was not a seat Labor was expected to win.
It comes as Opposition Leader Peter Dutton unveiled changes to the shadow cabinet following the Liberals losing the Dunkley by-election on Saturday.
The reshuffle saw MP Melissa McIntosh, who holds the seat of Lindsay, promoted to the shadow cabinet and will take on the portfolios of western Sydney and energy affordability.
Moderate senator Andrew Bragg was appointed to assistant home ownership spokesman while Victorian senator James Paterson will take on the role of shadow cabinet secretary.
Western Australian MP Andrew Hastie has picked up defence industry and defence personnel portfolios on top of being the defence spokesman.
Queensland MP Phil Thompson will become the assistant for both of Mr Hastie's new portfolios.
