How can I encourage...?

First, though not tagged D&D5e, the answers to these questions contain much valuable advice. I suggest you peruse them:

• How can I encourage role playing in a custom setting?
• How to introduce and encourage role playing in non-roleplayers?
• How do I encourage new players to be more descriptive in their actions and intents?
• As a GM, how do I encourage a party to interact with each other?

However...

There are many different games we play.

^{WARNING: AngryGM liberally salts his excellent advice and analysis with rude and vulgar language.}

It sounds like you want to play the game where "we throw ourselves into someone else's shoes and talk like them."

It doesn't particularly sound like this player wants to play that game.

That's okay.

At any D&D table of \$N\$ players there tend to be at least \$2N+1\$ games being played, in my estimation.^* Not every player equally enjoys each of those games.

The key steps for you to take are to discuss the following with that player, possibly with the entire group participating:

1. I don't see you engaging much in "acting" scenes--do you enjoy that time? (The player may just enjoy watching the show play out.)
2. Do you want to be more active during those scenes?
3. Are there parts of the game you wish we'd be spending more/less time on? (This is a good question to ask all your players, every session.)

And then use the answers to these questions.

Coda: System Matters

I feel I'd be remiss in not adding this: recognize that you're also playing in a system that's not really optimized for that game. Sure, D&D handles it, but it's not built around the sort of roleplay you're describing.

If your player really does want to expand their acting-game, and the things you can try within D&D don't work out, then you may want to consider fantasy-adventure roleplaying games that are built around play-acting.

^{* - note that number snuggles somewhere in between "more games than players" and "not as many games as pair-interactions" for \$N>3\$. \$N=2\$ and \$N=3\$ are special cases.}

I recommend not forcing your players to draw maps

From everything I have experienced with players new and old, having players make the maps doesn't work well and I would recommend not doing it at your table without careful consideration and good reason.

When making any change to your game, you should consider and be clear on at least a few things:

• What is my goal for this change and will the change accomplish that goal?
• What downsides or issues will be caused by this change and will that outweigh any potential fun from the change?

It's unclear what your goal is with this change and who it is for

As I wrote above, I would enjoy having them invest into drawing a map. But it's also for when they we'll need a map to don't get lost in a very big maze or else, for example if we play Waterdeep Dungeon of the Mad Mage.

As I will mention below, you should be very careful about crossing in-game and out-of-game challenges. But more than that, you don't seem to have expressed a compelling reason to need this beyond the fact that you (and currently only you) want it.

If you don't have a clear reason to make the change you need to be very careful that you aren't introducing issues for no gain.

Do your players want this change or just you?

You say:

For me it bring some realistic side (maybe my players will not like that, but that's not the point here) and I like it pretty much.

Right off the bat, this makes me concerned about the mindset here. You need to take into consideration the wants and needs of the whole table, not just for you, and the sooner you do the better. So whether or not the players will like it is very much relevant.

Talk to the players before going any further and figure out if this is even something they remotely want, because if they don't, then you are wasting your time and everything else is moot.

Forcing players to draw maps can have serious practical issues

To give context to the below list, one of my most extensive experiences with player mapping came from an enormous and complicated dungeon which the DM required the players to sketch out. We sketched each room to exact dimensions to grid level accuracy, which was often useful because there were encounters in many of them.

If you're situation is substantially different from this, the extent of the problems will certainly vary. However, I think these problems will have to be dealt with to one extent or another regardless of the context.

There are may be ways which could reduce some of the impact of the issues, but I haven't tested any and so won't address that in my answer.

Every one of these issues is one that has repeatedly come up at my tables throughout the years.

It takes a lot of time

I'm not joking when I say this, even in a simple dungeon, having the players draw maps can and likely will slow progress to a crawl. This is because it requires the DM to give all the information about the room (dimensions, locations, doorways, location on the map, etc.) while the player is sketching. During this time the DM could instead be describing the room narratively, interacting with the PCs with their actions in the room, looking at encounter information, reading ahead, or literally any other productive task. Instead, they are describing a map which they have drawn out in front of them to someone else who can't see that map. Even if the players hear and translate that information perfectly onto the map, this still takes precious time away from a session that could be used for other things.

At tables I've played at, the time it takes to draw the map out in real time has been a large source of frustration even among people that enjoy making the map.

Mistakes will be made

No matter how obvious you think your description of the room is, the map-drawers will accidentally get it wrong. A lot. They'll do things like accidentally flip width vs height, put the door on the wrong side, attach the room on the wrong wall, etc. And when they do you have to spend even more time to have them erase it and then correct it. This happened once in an error so bad the DM had to take it home and sketch a decent portion of the map again.

And that is if you manage to notice the error. Many times I've had DMs not notice until hours later that a mistake was made on the map and now suddenly this room won't fit! You think this won't happen to you, but it will. DMs are busy and even if you take (even more) time to check over a drawing, you too will miss errors (a common source of DM error: the fact that you are looking at their map "upside down").

Sometimes, you will end up just giving up and (re)drawing things for the players because of misunderstandings in which case you might as well have done that from the beggining.

It's only interesting, at most, for one player at a time

You mentioned worrying about players not paying attention before. Well this is a great way to get them to pay even less attention.

It only takes one person to draw a map and it isn't particularly a thrilling process. Even if the group is theoretically interested in doing this, only one person gets to do the fun part, and the rest of the group is left with nothing to do. Expect phones to come out and people to leave and get snacks or drinks while this occurs. This is the opposite of one of the things you mentioned wanting to do which is to keep their attention. At most, you get one player's attention and lose the rest of them while things are worked out. I have personally experienced it both as the checking out player and observing others doing the same.

New players have enough to keep track of

You mention this is for new players. This is going to be a challenge to them but they likely will already have their hands full trying to learn and manage their characters and new abilities and roleplaying. Having them take time away from that can lead to less-prepared and engaged players.

Using IRL challenges to represent in-game abilities can be problematic

I'm talking about players physically drawing a map, not only their characters.

You say that, but then most of your question is dedicated to introducing how this real-life map will affect the in-game world and the PCs. This is an issue you need to sort out. Unless you have player buy-in, real-world challenges should not affect the abilities or successes of the PCs in-game. Or, at the very least, that line should be clear and made apparent to your players and only implemented with their explicit buy-in.

Players generally play games because they want to do stuff that they are not capable or wanting to do in real life. Making game challenges depend on real-world successes means that players who aren't good at that task get their in-game characters punished unjustly.

So, if this is your main motivation for doing this, please reconsider.

I think it's much realistic and interesting to test the real memory of the players instead of assuming their characters remember everything they see.

You don't have to assume that a character remembers things perfectly, but the game already has mechanics in it to address that. The characters can draw maps just fine without having to have the players do so in real life. You can even simulate this with a survival or some other check (or a series of them).

Think of it this way, what if one of the PCs was a map-drawing master. An explorer by trade with an unerring sense of direction (a Ranger, say). What sense does it make to make that PC's map-making success depend on the result of the players' skills? Will that enhance the fun at your table?

Conclusion

I don't recommend doing this because, in my experience, it is a whole lot of hassle for potentially (if not entirely) no positive gain in fun for the table. Forcing players to draw all the maps has a lot of potential pitfalls and many groups won't find enjoyment in it.

Here's what you should do before considering proceeding with his idea:

• Reevaluate why you want this to happen. Challenging the players instead of the characters is not a good reason and will likely not resonate with your players and lead to frustration. If you are going to introduce this, you need a good reason, one that is fun for the whole table.
• Talk to your players. If they aren't interested, this idea is a non-starter regardless of what you personally want. If they are interested, you need to talk to them explicitly and in-detail about how this will work and make sure they agree to it and that it seems fair.
• Once you've done that you are going to need to tackle the practical issues I mentioned above. Problem is, I've not seen any great solutions. If you don't tackle them, you need to prepare for longer sessions and less engaged players.

tl;dr

In the end, having players draw maps is not going to kill your game or drive your players away (likely). However, if you're going to do it you have to do it for the right reasons, with player buy-in, and with an awareness of the potential issues.