Judging by what you want to do I would do it a bit differently actually.
You have 2 layouts. The menu & the game.
You startup with the menu.
You make a global variable "current_player". By default it is empty.
On start of layout of the menu you check if the current player is empty OR the list is empty. If so, you just show the menu and allow adding players to the list.
You've got a button to start off with the first player. When you press it, a person is selected from the list, the current_player variable is set to that value, and you go to the next layout. There you can read the current_player's name from the variable. In the game layout you foresee a possibility to go back to the menu.
On start of layout of the menu you check if the global variable is empty. If it is not empty, you know the menu is loading because it is coming back from the game layout. So you check if the list is empty. If it is not empty you immediately choose the next player and go to the game layout again after setting the current_player again.
The last time you load the menu again, the list will be empty, and you just snap into the logic where the game started off to begin with.
That's my 2 cents.
If you're completely new to this, maybe you can check my tutorials on my channel, where you can get a good understanding on how you can make some real world example games and how the logic could work.