Hi Stirletz and welcome,
You could always start your trip somewhere else, SE Asia has become one of the more difficult places to travel with your own bike. As to buying in each country it is very easy to rent in most of them, even crossing borders with local bikes is not always easy so buying might not help.
Myanmar has actually got easier than a few years ago when no travel with your own vehicle was allowed, China was also out of bounds to all but backpackers until travel with a guide was allowed.

The first question thats comes to mind is WHY do you want to start your trip in the country that has been the most difficult country towards overlanders the last year? The most discussed countries on forums as well as facebookgroups?

Do yourself a favour - start somewhere else. Why not start where you come from? I wouldnt ship my own bike to Thailand - even if I got paid to do it, which is costly enough just to be honored by having to pay for guides, permits, paperwork an mass which also is very expensive and then be very restricted to your guide. And neighbouring countries can also be hard to go through as well. Myanmar - guides and permits needed, Laos not too bad but a bit restrictive to let in foreign vehicles through certain bordercrossings, Cambodia - well seem to demand Carnets although not a Carnet country and in most other cases also permits from central authorities in Phnom Penh, Vietnam - has been as good as impossible to get into but maybe it has become a tad easier nowadays - officially you need an expensive permit, some guys have been able to enter without, but I wouldnt count on either of this options to be honest, China - permits and guides needed and very expensive, Malaysia - Carnet needed difficult to get mandatory insurance and kind of an dead end cause you need shipping to take you further.

To sum it up - to start in the most inconveniant country in the most inconvenaint part of the world seems TOTALLY UNLOGIC to me. But of course others could have another opinion.

To buy a bike in Thailand as a foreigner is possible but not easy. You need an official adress (recidency sertificate) which is not always easy to obtain, especially on a tourist visa or a visa excempt which I presume you will be entering the country with. But if you are lucky enough to be able to buy a thai plated bike on ylur own name you should be able to take that thai plated bike into Malaysia, Laos and Cambodia. Other countries would be difficult. Mind you - Laos normally dont let in smaller bikes of 125 cc and less (since Thailand dont let in Lao plated bikes 125 cc and less) so you will need a bike of lets say 200 cc at least.

If youre thinking about taking a thai plated bike for long distance travel Im not sure how that would work out. For example - where to get a Carnet for a thai plated bike? I think thats impossible my friend - but prove me wrong if possible.

A Vietnam plated bike should be possible to take into Laos and Cambodia but not Thailand. Although in these parts of the world you never know. Into Thailand is normally not allowed. Some "smart" backpackers have paid locals to take their vietnamplated bikes across the borders to Thailand and then continued themselves - unneccesary to say this is very illegal and will only make it harder for lawobeying travellers in the future.

Thailand is lead by a military junta that does exactly what it wants, China is a one party communist state and Myanmar are still run by a military government that still supress political activity especially amongst etnical minorities - so what can one expect from those countries.....?

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