Can a perimeter be built in the cloud, and what should you expect when you do?

Yes. The large cloud providers (Azure, AWS, Google) offer every common network component needed for a perimeter (virtual Layer 1-3 devices such as networks, routers and firewalls) as cloud services. They often carry unusual product names and may be limited in function compared to their hardware counterparts.

The perimeter model is not tied to your own data centre. You rent virtual networks, subnets, firewalls and VPN gateways and configure them like their physical equivalents. Two practical consequences: the team must learn the provider's own vocabulary and products, and you must check what a virtual component cannot do before relying on it, because the offerings change often.