Animals, even ones that fly in cabin, must go through the animal quarantine office at BKK airport for inspection upon arrival. Can take an hour while you wait your turn for an officer, depending on how busy it is.
the OP is using an agency that is supposedly hiring people, to qualify them for non B visas, so the agency is limited in how many they can do under whatever sham structures they've created to get around the law.
You can use Grab, Bolt or InDrive. Compare prices in all 3 apps. Can vary by over 30%. Or just use a metered taxi from the airport's official queue system. Highly organised and easy.
Many people have suggested one of the onward ticket sites. Just be aware that every onward ticketing site only makes an on-hold reservation that shows as pending, not an actual paid ticket with an e-ticket number. This means there is always a chance that a knowledgeable person reviewing your proof of onward travel will know it isn't a valid ticket and is nothing more than a hold. You could actually do the same thing yourself by booking a flight on any airline website that allows a ticket hold for a few days or that allows a ticket hold to pay at the counter or at a store. It would generate the same reservation with a valid PNR booking code pending your payment. If you are using it at an airline check-in counter when they ask for an onward ticket, the check-in staff usually knows to look for an actual e-ticket number as PNR codes don't indicate it is an actual ticket. Onward ticket sites work well when applying for visas where consulate officers typically don't know the difference, but it is risky using it at an airport check-in counter when you have a one way ticket.