I want to create an Application Control Global Ruleset, however it seems to be the only kind of policy which cannot be created through the Management Console, only via the API access (which is not configured at the moment for my organisation).
Did I get something wrong, or is the creation not possible through the console?
You are correct, creating Application Control Global Rulesets is handled through the API.
More information on this:
As an aside, you mention that the API is not configured for your organization. Getting started with the API is very doable, and there's more info in the articles starting here: https://automation.deepsecurity.trendmicro.com/article/dsaas/first-steps-for-deep-security-developers?platform=dsaas
(I work for Trend Micro)