lmao
Yes you can.
The actual state space is 8 with 67 zeros. (That's 52!)
And you don't have just one deck, you have 10^30 of them.
If it takes you ten seconds to shuffle a deck, you get about 3 million shuffles per year, per deck. Therefore the Poisson equation says you're likely to repeat a result within 10^15 seconds or so.
How long is that?
How many seconds in a year?
Answer: 60x60x24x365 = about 31 million.
10^15 divided by 3x10^7 is very roughly about 100 million years.
So there you have it. You are well within the evolutionary time frame.
The fallacy in your logic is, you don't just have one deck of cards.
10^30 is the number of microbes on earth. But the number of reactive carbon atoms in the ocean is vastly greater than that, it's on the order of 10^55. You can do the math on that too.
Carbon atoms only have 4 configurations instead of 52, and you have 25 more orders of magnitude of them.
So you see, your math is entirely fallacious, as Abu pointed out. You failed to account for the multiplicity of simultaneous experiments.