First of all, the problem of humans using too many of the world’s resources.
Me: Obviously this is no good because there’s no verb.
You: What about ‘using’? Isn’t that a verb?
Me: Sometimes yes, but here it functions as a noun modifier, not as a verb. It’s telling you something about the noun ‘humans’. It’s part of one long noun phrase: ‘the problem of humans using too many of the world’s resources. If you want to you can use this long noun phrase as a subject:
..or as an object:
In future make sure your sentence has at least a subject and a verb.