Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Bangkok to Havana as you normally would.
Havana Jose Marti Intl (HAV) is the airport you will fly into if you book a flight from Bangkok to Havana. You should not have trouble finding flights to Jose Marti Intl from Bangkok; the airport handles an average of 0 inbound flights from Bangkok per day. You should also have plenty of airline options to choose from since 0 airlines have flights to the Havana airport from Bangkok. It is only a 15.7 km journey from Jose Marti Intl (HAV) to Havana’s city centre.
This is defined as Bangkok Suvarnabhumi Airport (BKK) and Havana Jose Marti Intl Airport (HAV). Codes like Havana Jose Marti Intl Airport are often used to just call airports uniquely. Bangkok Don Mueang Intl Airport (DMK), Rayong Utapao Rayong Pattaya Airport (UTP), Hua Hin Airport (HHQ) are other airports near this flight route and their unique identifiers/IATA codes.