The symmetry-breaking first-order phase transition between superfluid phases 3He-A and 3He-B can be triggered extrinsically by ionising radiation or heterogeneous nucleation arising from the details of the sample cell construction. However, the role of potential homogeneous intrinsic nucleation mechanisms remains elusive. Discovering and resolving the intrinsic processes may have cosmological consequences, since an analogous first-order phase transition, and the production of gravitational waves, has been predicted for the very early stages of the expanding Universe in many extensions of the Standard Model of particle physics. Here we introduce a new approach for probing the phase transition in superfluid 3He. The setup consists of a novel stepped-height nanofluidic sample container with close to atomically smooth walls. The 3He is confined in five tiny nanofabricated volumes and assayed non-invasively by NMR. Tuning of the state of 3He by confinement is used to isolate each of these five volumes so that the phase transitions in them can occur independently and free from any obvious sources of heterogeneous nucleation. The small volumes also ensure that the transitions triggered by ionising radiation are strongly suppressed. Here we present the preliminary measurements using this setup, showing both strong supercooling of 3He-A and superheating of 3He-B, with stochastic processes dominating the phase transitions between the two. The objective is to study the nucleation as a function of temperature and pressure over the full phase diagram, to both better test the proposed extrinsic mechanisms and seek potential parallel intrinsic mechanisms.