This is a head-spinning question.
MIT Technology Review article points out that training the model uses much more resources than using it afterwards. Based on their data for BLOOM, training took as much resources as running it for a bit over 7 years straight. So the basic strategies are obvious - limit the number of models that have to be trained, share already trained models, use them as long as possible and always prefer using already trained model to training the new one.
This article also points out the difference between energy usage for training and total cost of training, which would also include costs of manufacturing equipment and costs of infrastructure. This is where things start to become complex, because it’s only fair to assume that some of these costs would be paid anyway - some of data centers, servers, graphics cards, routers, electricity etc. would be produced anyway, they would just be used for something else. So you would need to compare actual AI usage with some hypothetical other usage, including the real and predicted benefits of both. I don’t even have a good idea where to begin.
We can’t talk about minimising resource usage without mentioning Jevons paradox - this is when developments in efficency cause increase in demand so large, that eventually total usage is increased instead of reduced. This is what we observed with coal usage in 19th century. This is not inevitable and I don’t think there are any hard rules that allow to predict whether it’s going to happen or not, but there is a risk that any efforts put into minimizing AI natural resources usage will actually only increase them.
Finally, I don’t think the discussion should be limited to carbon footprint. Data centers are known to use large amount of water, and big tech companies are securing tax benefits disproportionate to number of jobs created. Sure, these data centers are not used for AI exclusively and both of these were problems before current surge in AI usage. But it can’t be denied that AI is contributing factor now.