I've took my two French Bulldogs (snub nose) from USA to Thailand last year (2023),
You will need to get a livestock import permit for each pet and a health certificate for each pets stating they have the required vaccines. Also, the certificates must be dated no more than 30 days from your arrival (maybe less).
The next hardest part is finding an airline that will take you pet. I had business class on Qatar but they would not accept snub nose in cabin or in the hold. I had to switch to Turkish Airways which allowed snub nose dogs. The hardest part is timing as Thailand will only accept the original health certificate and the date on the certificate has to be with a certain timeframe.
You will have to go to the livestock quarantine station with all your paperwork. I flew into Suvarnabhumi and the station was behind baggage check 3 I think.
The hardest part for me was the initial check-in at Miami. I had no less than 5 different people ask of my paperwork. Just have multiple copies of everything and keep all your originals for when you arrive in Thailand.