Frog and bird can move before space bar is pressed.

private bool gameStarted = false;
[SerializeField]
private Text gameStateText;
[SerializeField]
private GameObject player;
[SerializeField]
private BirdMovement birdMovement;
[SerializeField]
private FollowCamera followCamera;
private float restartDelay = 3f;
private float restartTimer;
private PlayerMovement playerMovement;
private PlayerHealth playerHealth;


// Use this for initialization
void Start() {
    Cursor.visible = false;

    playerMovement = player.GetComponent<PlayerMovement>();
    playerHealth = player.GetComponent<PlayerHealth>();

    //Prevent the player from moving at the start of the game
    playerMovement.enabled = false;

    //Prevent the bird from moving at the start of the game
    birdMovement.enabled = false;

    //Prevent the follow camera from moving to its game position
    followCamera.enabled = false;
}

// Update is called once per frame
void Update() {
    //If the game is not started and the player presses the space bar...
    if (gameStarted == false && Input.GetKeyUp (KeyCode.Space)) {

        //...then start the game
        StartGame();
    }
    //If the player is no longer alive...        
    if (playerHealth.alive == false) {

        //...then end the game...
        EndGame();

        //...increment a timer to count up to restarting...
        restartTimer = restartTimer + Time.deltaTime;

        // ...and if it reaches the restart delay...
        if (restartTimer >= restartDelay) {

            // ...then reload the currently loaded level.
            SceneManager.LoadScene(SceneManager.GetActiveScene().buildIndex);
        }

    }
}

private void StartGame() {

    // Set the game state
    gameStarted = true;

    // Remove the start text
    gameStateText.color = Color.clear;

    // Allow the player to move
    playerMovement.enabled = true;

    //Allow the bird to move.
    birdMovement.enabled = true;

    //Allow the camera to move
    followCamera.enabled = true;
}
private void EndGame() {
    gameStarted = false;

    //show the game over text.
    gameStateText.color = Color.white;
    gameStateText.text = "Game Over!";

    //Remove the player from the game
    player.SetActive(false);
}