I find, during character creation for new or "quiet" players, ask them who their "storybook" heroes are, who would they like their character to be like?
Sir Sparhawke, Raistlin, Jimmy the Hand from Magician, etc
Then have them base a character on that, someone who they can associate with, when something happens, they can think "I know what Jimmy would do in this situation" and they will be excited to see their version of Jimmy / Sir Sparhawke / etc performing that role.
Also, if we've had a new roleplayer join us, I will have a word with one of my more experienced players and have them "mentor" the new player; have their character interact with the new player's character;
The Experienced player will introduce themselves in game, and help the new character have a "conversation" with their character "in game", not as John and Peter, but as Sir Sparhawke and Raistlin (or whatever their character names are).
The experienced player will also help them with game mechanics and help them with options and encourage them along (as all other players should).
I encourage first person play, where a player will say "I am throwing this spell / firing my bow / etc" rather then "My character is throwing this spell / firing their bow / etc"
I think as soon as you can start having your quiet new character thinking through their character, they will enjoy it more.
Often, we will send the "new player" off to buy supplies before they leave on their quest / expedition / rescue / etc with a list of "things" from each of the other characters, and I will turn this into a "mini-adventure" for the new player, with LOTS of interaction with NPC "characters", from a dodgy pie saleman (ala Mr. Cut-Me-Own-Throat Dibbler from Ankh-Morpork) to a "lady of the night".
This also helps them develop a character on their own, and gives them a sense of purpose, as well as not having to make an "end of the world" decision. They get to haggle ("You must Haggle" from Life of Brian, is ALWAYS a favourite to bring them out of their shells ... humour works for everything).
But most of all, it is about bringing a FUN experience to the quiet / shy player, be patient, encourage them, and they might just surprise you ...
Have fun playing ...