Serverless computing offers elastic scaling and pay-per-use execution, making it well-suited for AI workloads. As these workloads run in heterogeneous environments such as the Edge-Cloud-Space 3D Continuum, they often require intensive parallel computation, which GPUs can perform far more efficiently than CPUs. However, current platforms struggle to manage hardware acceleration effectively, as static user-device assignments fail to ensure SLO compliance under varying loads or placements, and one-time dynamic selections often lead to suboptimal or cost-inefficient configurations. To address these issues, we present Gaia, a GPU-as-a-service model and architecture that makes hardware acceleration a platform concern. Gaia combines (i) a lightweight Execution Mode Identifier that inspects function code at deploy time to emit one of four execution modes, and a Dynamic Function Runtime that continuously reevaluates user-defined SLOs to promote or demote between CPU- and GPU backends. Our evaluation shows that it seamlessly selects the best hardware acceleration for the workload, reducing end-to-end latency by up to 95%. These results indicate that Gaia enables SLO-aware, cost-efficient acceleration for serverless AI across heterogeneous environments.