Hmmm, that's a hard one. I don't know how much money you have but it's gonna be really hard to do Thailand-Greece overland with less money than what it would cost flying, I'd say impossible. But it would be a great adventure for sure.
There's not too many ways to go overland from SE Asia to Europe. And something you need to make sure is that your girlfriend can get visas for the country mentioned below. Kenyan passport is not the best to travel unfortunately and she might find that she can't follow you in because of visa regulations.
First, the boat option is pretty much out. Cargo ship is expansive and hard to find and cruise ship is even worse. Unless you have contacts, it's not gonna happen. Maybe you can post something on TT Ocean forum asking if anyone sailing around the world could pick you up or something but I wouldn't count on it.
Crossing Burma into India is impossible. If you want to go the Indian route overland you need to go through Tibet and Nepal and I'm sure the 300$ permit to get into Tibet is too much. You could try to sneak in Tibet without paying the permit, few people have done it without problem from Golmud although it's not without risk. There's also very cheap flights from Calcutta to Bangkok if you're willing to forget the all overland part. If somehow you manage to make it to India, then it's fairly straightforward fast overland route (India--->Pakistan--->Iran--->Turkey--->Grece). It might be hard to obtain Iran visa as american, would be easier if you have greek citizenship I think. Calcutta-->Greece can be done overland in 10-12 days if in a real rush.
There are 2 other routes that are a bit easier, although I don't know how they are in winter. They're close to what Poz recommended although Russia Georgia crossing is not open to foreigner (if you're REALLY adventurous, there's a thread on TT about people who managed to cross it by going through the unrecognized republic of South Abkazhia but I suggest you learn russian if you want to try that).
1) SEA -> China -> Kazakhstan (ferry to) -> Azerbaijan -> Georgia -> Turkey -> Greece
Visas shouldn't be a problem here. Only problem is I don't know if the ferry from Kazakstan to Azerbaijan runs in winter, and that Kazakhstan is fairly expansive (too many oil expats)
2) SEA -> China -> Mongolia* -> Russia -> Bulgaria (there's a direct train Moscow Sofia) -> Greece
*Mongolia can be avoided if you take the trans-manchurian line of the transsiberian if you don't want to get their visa.
Again visa shouldn't be a problem here, although I would arrange the russian visa in advance as Beijing embassy will not give them to you if you're not chinese (your name give a little hint that you're not). This is probably the easiest, cheapest and most sensible option.
Good luck with that adventure mate. Hope my post helped and keep us updated on what you decide to do.
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