First off, I don’t believe Vassal will automatically distribute cards when you start a new game. However, you can place a “Setup” button on the map somewhere (something I do all the time) and when you click it, it will set the game up as you like and you can have the button delete itself once it’s done.
I’ve posted a few example sample mods in the past. Here’s some links to those threads. Most are quite simple but they should give you some insight into manipulating cards.
https://forum.vassalengine.org/t/send-cards-from-one-deck/8594/1
https://forum.vassalengine.org/t/randomized-board-layout/6270/1
https://forum.vassalengine.org/t/adding-tokens-to-predetermined-locations-via-a-button/4257/1
https://forum.vassalengine.org/t/how-to-deal-to-hands/3836/1