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Server with GPUs are expensive because no provider wants to turn their datacenter into someone else's mining rig. You can get them, but they'll cost you.

In Hetzner's case, you'll find some with GTX 1080 (https://www.hetzner.com/sb?additional=GPU), but they'll cost you at least double of what they'd cost without one.

You can definitely run a Cloud VM with GPU and pay by the second. I've used Google Cloud for this and it works very well

GPU instances do exist on all major providers. I used some on Azure for sure.

If you just want to play with DL, I suggest Google Colab Pro.

Lots of GPU Clouds around. To play with toys I use runpod's community cloud. Very affordable.