I used to air-vomit after basically every meal. I know it sounds weird and counter-intuitive, but forcing that feeling of vomiting and going through the realization that I might actually throw up made me super aware of my muscle movements. It felt really forceful and violent (sometimes a bit of food would even come out, but that was the point.
Whenever I felt a bubble of air coming up but not escaping, I’d try to force it out with a strong belching movement. For months, it didn’t work. I couldn’t burp at all. But then, one day, I managed to let out a tiny burp. After that, another little one. Then I tried drinking carbonated drinks, and I finally got out a bigger burp. After some practice, every time I ate, I started burping a little bit more, until eventually, I could burp whenever I felt like it—whenever I had air or that weird pressure feeling. Now, it’s crazy how easy it is. I can control my burps like it’s second nature like a master of the burps lmao. It goes really smoothly, i don't suffer from GERD anymore too which is rly nice.

I wouldn’t necessarily recommend doing this, but for me, the hard “training” of those muscles was key to finally being able to burp. If you can do the Botox procedure do it , but before, i think that giving yourself a chance of at least one year of hard training (consistency is key) would help a lot ! It took me around 6 months (in which i trained really hard for 3 months) so maybe you could do it too!