[RPG] Is it possible to start a character with tremorsense? What kind of negative stats would I need to take?

I can't say whether this, on its own, will change your players reactions (at the end of the day, gold is just another number on their character sheets). Certainly, I know it wouldn't interest most of mine - They'd just think "Oh, hey, our riches are 90% easier to carry, now," because assuming easy access to money-changers, the only thing you're really changing is the weight of it. That said, this does make a single gold piece have more meaning and value in a player's mind, as it goes from being "about a day's living expenses" to "enough to feed and house the entire party".

Whether it changes their reaction to finding gold depends on the precise details of your implementation. For instance, if you keep the number of gold pieces per cache the same, but only give out gold caches 1/10th as often as you currently do, your players are more likely to treat each cache of gold as a rare and fabulous treasure; On the other hand, if you give out gold caches just as often, but give out 1/10th as many gold pieces in each one as you do now, players will see gold as a convenient but rare high-denomination coin.

Besides changing the value of coins, there are other things you could do to make gold pieces seem more special. For example, in one of my current campaigns, players generally deal in gold, silver, and copper, but almost never in platinum. This is because I've declared platinum to be so rare that it's almost never used by NPCs in the setting, and therefore they can't find anyone to change their smaller-denomination currency into pp. A platinum piece still isn't any more valuable than the standard 10 gp, but because players only ever find them in rare treasure caches, they have a tendency to hoard them and treat them as precious.

Another traditional strategy to make coins more interesting is to give them names and states of origin; There's more flavour in a bag of Linnish Sovereigns than in the same-sized bag gp, and if there's a single Avench Groat in there - well, there's surely a story behind that, right? In your case, you could declare that no gold coins are minted locally, and that all gold coins therefore come from some exotic foreign land. The novelty would likely wear off sooner or later, but it'd be a start.

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.

versus

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.