I would have all the supporting documents they may ask for ready beforehand, and also get the documents officially certified.
Like your bank statements etc. Even if you don't need them, it really speeds up the process when they ask for them.
In many cases, this involves obtaining an affidavit to specify the documents you want officiated, and most Thai Royal embassies may request this but also accept affidavits from the home country's embassy, even if it's in another country.
I had them request this in Malaysia and it took two extra weeks as I had to make an appointment at the US Embassy in Kuala Lumpur to do this.
Anonymous participant 468, did you do the complete verification so you could access the entire assortment of banking features? They will ask for supporting documents. If you haven't done this yet, that's possibly why you can't add a card.