Is it permissible to work as a design engineer for HVAC networks in an aquatic sports complex that will host an international competition, in which it is highly probable there will be competitions for women?

If it is highly probable that the design will be used in something forbidden (haram), then it is not permissible for you to create it, due to Allah's saying: "And do not cooperate in sin and aggression." The dominance of probability takes the ruling of certainty, and aiding someone who commits an evil act is a sin. The Wise Lawgiver has blocked the means leading to what is forbidden, making the means subject to the rulings of the ends. Therefore, in the matter of intoxicants (khamr), everyone involved, from the drinker to anyone who assisted in it, was cursed, and similarly in the matter of usury (riba), because they are cooperators in sin. So, abandon this matter, and whoever gives up something for the sake of Allah, Allah will compensate him with something better.