Robertlandy Simon Aties and Marlon Yant Herrera scored 14 points for Cuba each and Iran’s Meysam Salehi earned 15 points.
Team Melli, led by Mauricio Motta Paes, will play Argentina early Monday.
Poland tops the world rankings and are also the defending champions, winning their first VNL title last year. Since the inception of the league in 2018, the host nation has finished in the top three on four out of five occasions.
In the preliminary round, the 16 teams are divided into two pools, which are reshuffled for each of the three weekly phases. Each nation will play 12 matches in the pool phase, with all results combined into one ranking table.
The top eight teams will then qualify for the knockout stages in Poland, with the bronze and gold medal matches taking place on 30 June.
World Ranking Points will be awarded or deducted after each match of the preliminary rounds of the competition and this will be important for some of the teams who haven't qualified for Paris 2024 yet: five additional Olympic quotas will be decided using the FIVB rankings in June 2024.