You don’t need FTL travel or multi-generational ships really. If you get close enough to the speed of light, time dilation can make the travel time for the people on the ship be as short as you want. Only for the people that stay on earth would the spaceship appear to take generations. Getting enough energy to reach such high speeds would be the difficult part as well as accelerating quickly without crushing the travellers.
There is a route from Europe to China that avoids Russia. But it has to take a ferry from Kasachstan to Azerbaijan. There is no Rail connection through Iran as far as I know. Then it goes through Georgia and turkey. I don’t know the exact route from there. But I think there is usually another ferry necessary from eastern turkey/georgia to Europe even though there would be a land connection and Bridge from turkey to Greece. But I think the ferry is easier because they would have to change the train anyways between Georgia and turkey due to different rail Gauges.
Even in countries with universal health care surgeries aren’t typically free. They are just paid by a public health insurance. That health insurance will pay at first but it will try to get it’s money back from you if you injured somebody.