The next generation of wireless mobile networks will be driven by software and infrastructure virtualization. At the same time, the underlying hardware will become more diverse. Edge, intermediate and central network nodes will allow distributed deployments of never seen before scale. Non-terrestrial networks, nomadic networks and networks in networks promise more dynamicity, changing their topologies over time in predictable and unpredictable ways. To handle the complexity and dynamicity, a highly flexible and adaptable network is required. The key enablers of this complex digital communication system will be programmable infrastructures. From programmable access and flexible backhauls to zero-touch, adaptable and resilient control planes, we conducted research into advanced programmability at different layers of the network, within the Open6GHub project. In this article, we present innovative solutions for advanced programmable network infrastructure and show why they are essential for our vision of the programmable infrastructure of future wireless mobile networks.