I've had friends who received it a day or two afterwards. No idea why, though I did receive mine immediately.
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My friend, I've now had the game for 8 days and still no Coldheart
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That's wild. I'd double check and make sure any and all codes have been redeemed. They might be in an email or on the receipt. Then, check your respective digital store on console for any possible missed dlc downloads. If that doesn't work you might need to contact support for your console regarding digital downloads.