With the top eight from each of the three heats progressing and then next 12 highest points' scorers, 2011 world junior champion Cooke placed seventh in qualifier B in Palm Springs to advance.
He will be joined in the final by World Cup debutants Sam Curry and Joe Evans, who ranked eighth and tenth respectively in qualifier A, however there was disappointment for Tom Toolis.
Toolis, also making his World Cup bow in California, finished 12th overall in qualifier B which just edged the 20-year-old out of an appearance in the final.
Britain's women's quartet of Katy Burke, Heather Fell, Kate French and Jo Muir are next in action in Palm Springs and Pentathlon GB performance director Jan Bartu was buoyed by the team’s start.
"It's been an encouraging start to the first World Cup for the whole team in the beginning of the new Olympic cycle," said Bartu.
"I've been particularly impressed by the performances of Sam and Joe in the fencing. They took no notice about world champions or accomplished athletes. They were very good and it was refreshing to see.
"Jamie fought back after the fencing. It wasn't a particularly good semi for him, but hopefully he will take the opportunity in the final to rectify what went wrong in the semi.
"Tom narrowly missed qualification into the final by one position. There's room for improvement in his performance. Overall, a very positive day and I hope the girls follow suit in their heats."
- Sports & Recreation