Before the game
Make sure you are all on the same page before that game start. Explain that you want to play a serious game with lots of immersion. State that you are both willing to help others with immersion and lead by example. This is best done before the game starts. If not all players agree, then you might want to rethink join said game.
As a side note, new players might not be fully cognisant of all the intricacies of the same page tool. This is but a chance to explain to them the differences between play styles. The new player might not know what they want but a hint is better than nothing. A small word of warning that the same page tool is not meant to be a survey of what is wanted but a way to build a consensus on what they want to play. The aim here should be to give new players as much knowledge as you can to help them make an informed choice as to what to try. Descending into a lowest common denominator where no one is happy is a sign that you want different things: this is fine too.
During the game
Some new players can be intimidated and not wanting to be perceived as ridicule themself, make fun of others. So, the more experience players need to show that it is not worth of ridicule (even if it is silly) and encourage said new player to play a role, however silly that role might be.
We all have seen and read much fiction and finding a stereotype to play ("Your character is Conan as played by Arnold Schwarzenegger") might be helpful. It is easy to see how said barbarian would act in a given situation.
Show new players the difference between:
My character moves to the rocks to get a +2 to defence from bandit's arrows.
You bandit dogs! I run and jump under the cover of rocky formation, setting dust as I land. Scum! You made me dirty!!! You shall pay with your worthless lives!
Another idea we tried many times is to always be in character: even when you ask for the bottle, or chips, or say you're going to the loo. There is nothing funnier than trying to stop Conan ordering pizza over the phone! ☺
Props can help here or they can hinter -- I happened to be at the receiving end of either reactions without being sure why it worked once but not the other time.
Finally, one encourages timid players to role play in the same way one encourages them to do anything else. However, these methods are beyond the scope of this answer.