I've been struggling to find various ways to help one of my players immerse themselves more into their character and the world at large. A little bit of background, I'm running DnD 5e, and this is my first time DMming a big campaign. I'm leading a campaign for a group of five, with three veterans (two very seasoned players with plenty of campaign experience), and two people who are entirely new to DnD. One of the new players is a naturally quiet person, and insisted on joining and playing with everyone, which is great! I wanted to create a really good first experience for the two of them. Overall, everyone enjoys the experience (i've talked to each one extensively outside of the game), including said person. I feel like since it's his first time really doing any of this, he's struggling with playing and immersing himself in character. He is usually extremely reserved and doesn't open up to a lot of people, and has low confidence when it comes to improvising and playing a character.
However, during our sessions, he talks very little, and I've been trying a lot of different options and methods to get him more involved, ranging from giving him plot hooks to asking him directly what his character would be doing. He gets flustered and gives back an extremely vague and directionless answer that, frankly, make it a little bit hard as a DM to keep a pace going.
For example, the group gets into a small town to rest before scaling a large mountain. Everyone else starts to look around and see what the town has to offer. I asked him after everyone has gotten a lay of the land what he wants to do, and I end up having to give him examples of what he could do. Keep in mind this is after the rest of the party has deliberately tried to show their own initiative in exploring the city. He decides to follow the cleric to the marketplace.
"You part the folds of the tent and your eyes set upon a wide accoutrement of weapons that line the shelves. In the center of the tent, lay a forge, whose chimney protrudes out of the tent. A man in your typical blacksmith attire works on...etc. What do you want to do?"
The Cleric immediately pipes up and says "I want to search for any sort of magical implements or weapons, maybe something similar to my spear."
Then I turn to him, who plays a ranger, and ask "you watch as the cleric scrounges sloppily through an array of pikes and halberds. What do you want to do?"
"Oh you know, nothing in particular. Just looking around...at stuff."
During encounters, I ask my players to describe how they attack, and he keeps to very simple answers and responses, but understands mechanics well enough.
I'm not saying this in a comparing way, but both me and my other players give great, detailed and rich descriptions and make spontaneous/fun choices, so I know that we are providing good opportunities to observe us and our choices. I've tried a lot of different things, and I'm a bit at the end of my rope.
How can I encourage, without being overbearing or threatening, a player to open up and help them immerse themselves into their character?