Then there is there is the possibilty that earth/life simply can't occur by chance. Let's take another view on the card principle. We have a jar with 26 balls made of lead and 26 made of wood. The lead balls are numbered 1 to 26 and the wood balls 27 to 52. If we shake the jar and then pour the balls into a tube a little bigger in diamter than the balls, then numbers won't work because the huge difference in the weight of balls will mean it is no longer purely mathematical and the bottom of the jar (after shaking) will be mainly lead balls.
If the sequence of the balls in the tube to equate to earth/life is for the balls to be alternate in the tube it will never happen.
Think of it this way. If we have water in a saucepan (and atmospheric pressure) and heat the water 50*C and even do it an infinite number of times we will never achieve boiling water.
But if earth/life could form by chance and the universe is infinite then there would have been an infinite number of earth/lifes which would also mean that there were infinite number where advanced life would have existed at the right time for us to have seen evidence.
On the other hand the universe might not be infinte and if so what occurs when you get to the end