Staminec would have counted as a regular squad member, given he was born after the cut-off date of January 1, 2001.
Cacace, 23, also would have needed to be picked as an overage player, but has not been released by Italian side Empoli for the tournament.
Instead, the trio of midfielders Joe Bell and Sarpreet Singh and defender Michael Boxall have been picked as the three overage players.
Bell, 25, has captained New Zealand at youth level and plays for Norwegian side Viking FK.
Singh, 25, has long been a star for New Zealand at youth tournaments, and earned a move to German super-club Bayern Munich in 2019. The attacking midfielder is a free agent after leaving German club Hansa Rostock.
Boxall, 35, is a standout defender in American Major League Soccer club Minnesota United, and has earned 48 senior caps for the All Whites.
The trio were all part of New Zealand’s side at the 2021 Olympics in Tokyo that reached the knockout stage for the first time, before losing to hosts Japan in a penalty shootout.
Elsewhere, fresh from their respective moves to England and France, the pair of goalkeeper Alex Paulsen and midfielder Ben Old are notable inclusions, as part of a healthy core from the Wellington Phoenix.
The Phoenix’s run to within one game of the A-League Men’s grand final has led to eight players being selected in the 18-man squad.
Defenders Finn Surman, Oskar Van Hattum, Lukas Kelly-Heald and Sam Sutton join Paulsen and Old, as do midfielders Fin Conchie and Matthew Sheridan.
Former Phoenix striker Ben Waine, contracted to English club Plymouth Argyle, is expected to lead the line.
Midfielder Matthew Garbett is another notable inclusion, playing his club football in the Netherlands with NAC Breda.
Impressively, 12 of the 18 players selected have been capped at senior level by the All Whites.
The OlyWhites will face hosts France, the USA and Guinea in the pool stage of this year’s Olympics.
OlyWhites squad:
Joe Bell
Riley Bidois
Tyler Bindon
Michael Boxall
Fin Conchie
Matthew Garbett
Jay Herdman
Lukas Kelly-Heald
Ben Old
Alex Paulsen
Jesse Randall
Kees Sims
Sarpreet Singh
Matthew Sheridan
Finn Surman
Sam Sutton
Oskar Van Hattum
Ben Waine