Domain reg. expired, domain taken. Can I recover my domain?

As others have said, there’s the UDRP, which is what the GoDaddy-linked answer is covering, but here’s from ICANN (the source, mentioned in GoDaddy’s policy): https://www.icann.org/resources/pages/help/dndr/udrp-en

Without knowing if his was for a business, or a service mark or trademark, or even some just-well-known name, AND without knowing your location, it’s hard to say more. In the US you could (IaNaL) pursue small claims court, at the cheapest, and try to make an argument that they registered it in bad faith; if they fail to show up I’d guess an order from the court to transfer the domain back to you in exchange for compensating the purchaser for a year of registration would be your best possible (but who-knows how likely; courts are fickle things) outcome.

Outside the US, your local laws might be nicer to you legally.

As per usual, the answer is lawyers. There's a procedure where you can make a claim on a domain and take it over from the current owner... but I'm not sure that "I didn't renew it in time" is a good enough reason. You'll have better luck if this is a commercial related domain and you have some sort of legal claim (ie: trademark) over the name.

See section 4 of this article: https://www.godaddy.com/legal/agreements/domain-name-dispute...

You can also see this: https://www.godaddy.com/resources/skills/what-is-domain-squa...

I have no affiliation with GoDaddy - they just came up in some Google searches.

Isn't there an time, where an domain is blocked after it expires? Why weren't you informed about the failed billing?