Paperspace Core + GPU aught to do it, but it's not exactly cheap. Decent for testing but chances are if you want to scale you're better off with a COLO of a custom GPU rig and VMware ESXi (or another virtualization software that supports GPU pass-through, like I believe Proxmox and XCP-NG? [Not 100% sure on XCP-NG]).
COLO as a small guy you can use something like Joes Datacenter because places like Switch, PhoenixNAP, etc. are going to want you to need 1/4 rack before they even talk to you. Joes will even take a regular desktop system and host it in their datacenter so that's likely the simplest way to start as any GPU VPS or Dedicated is going to be high priced.
Paperspace is $0.45/hour for starting GPU, or $337.50/month, so slap yourself together a desktop with an RX5700 XT or something like that. It'll pay for itself after a couple months as you might be in for $500-600 but hosting goes down to $50/month with 1gbps line (33TB/month), and if the project doesn't work you can always sell the system later on to recoup most your investment.