I would probably just set visible to false, in case you need to show it again or restart.
extends Control
func _on_Button_pressed():
visible = false
In terms of the player, probably have a boolean variable that tracks whether the game is started or paused.
var is_playing = false
func _on_Button_pressed():
is_playing = true
func _process(delta):
if not is_playing return
# do the rest of your gameplay here