Using Dependency Injection in MVC PHP

For loading classes I use PSR-4 autoload. In my index.php I use FastRoute component. In that index.php I create $db connection and pass it to the controllers.

call_user_func_array([new $class($db), $method], $vars);

In the controllers I receive it and pass it to the models and use it there. I know that is bad approach. DB connection that was created in index.php how can I use it in my models not pass it through controllers etc and without singleton instance of a connection? How can I use DI or DIC to set up db connection in index.php and get in all models?

index.php:

<?php

require_once 'vendor/autoload.php';

$db = new DbConnection(new DbConfig($config));

$dispatcher = FastRoute\simpleDispatcher(function(FastRoute\RouteCollector $r) {
    $r->addRoute('GET', '/users', 'UserController/actionGetAllUsers');
    $r->addRoute('GET', '/users/{id:\d+}', 'UserController/actionGetUserById');
});

// Fetch method and URI from somewhere
$httpMethod = $_SERVER['REQUEST_METHOD'];
$uri = $_SERVER['REQUEST_URI'];

// Strip query string (?foo=bar) and decode URI
if (false !== $pos = strpos($uri, '?')) {
    $uri = substr($uri, 0, $pos);
}
$uri = rawurldecode($uri);

switch ($routeInfo[0]) {
    case FastRoute\Dispatcher::NOT_FOUND:
        // ... 404 Not Found
        break;
    case FastRoute\Dispatcher::METHOD_NOT_ALLOWED:
        $allowedMethods = $routeInfo[1];
        // ... 405 Method Not Allowed
        break;
    case FastRoute\Dispatcher::FOUND:
        $handler = $routeInfo[1];
        $vars = $routeInfo[2];
        list($class, $method) = explode("/", $handler, 2);
        $module = strtolower(str_replace('Controller', '', $class));
        $class = 'Vendorname\\' . $module . '\\controllers\\' . $class;
        $routeInfo = $dispatcher->dispatch($httpMethod, $uri);
        call_user_func_array([new $class($db), $method], $vars);
        break;
} 

controller:

class UserController extends BaseApiController
{
    protected $db;

    public function __construct($db)
    {
        $this->db = $db;
        parent::__construct();
    }

    public function actionGetAllUsers()
    {
        $model = new User($this->db);
        echo json_encode($model->getAllUsers());
    }

model:

class User
{
    protected $db;

    public function __construct($db)
    {
        $this->db = $db;
    }

    public function getAllUsers()
    {
        $stmt = $this->db->prepare('SELECT * FROM user');
        $stmt->execute();
        return $stmt->fetchAll(\PDO::FETCH_ASSOC);
    }