It's not that I don't believe you, its just that in 2010 about the only way to generate a bitcoin address was with the bitcoin client software.
8 words and passwords weren't really a thing as far as I can tell.  bitaddress.org, brainwallet, paperwallets websites, online wallets etc weren't online in 2010.

About the only thing online back in 2010 was New Liberty Standard, MtGox, Bitcoinmarket and the other sites mentioned in this thread https://bitcointalk.org/index.php?topic=1800.0

You can use the wayback machine on archive.org to see what these sites looked like in 2010, to see if any if them jog your memory.
eg: New Liberty Standard   https://web.archive.org/web/20100528074505/http://newlibertystandard.wetpaint.com/

Bitcoinmarket mentioned in this article with screen shots: https://www.bullionstar.com/blogs/ronan-manly/dawn-of-bitcoin-price-discovery-2009-2011-the-very-early-bitcoin-exchanges/

I could be possible that whatever site you bought the bitcoin on sent you a pgp encrypted wallet file. I read that somewhere, but I have no experience in how any of these sites worked except for MtGox.

Anyway have a nice holiday.