Is there a way to make my player character reference-able from every script?

I would recommend Posting guidelines in #Help channel to post better organised info about issue, in this case code.

To your topic :

1.) you can extend your player in your script and get reference to it as class, and add the node into group

class_name Player
extends CharacterBody2D

Other script

var player: Player

func _ready():
    player = get_tree().get_first_node_in_group("player") as Player

2.)use export variable to get reference to node.

@export var player: Player 

Assign corresponding player node in inspector on the right side.

3.) last resort use Singleton/Autoload.