Quote

Years ago, I sent some Bitcoin to an address without any physical backup, to see if I could find it back years later. Now, I can't find them back. Lol.

Yes, it is quite common. Having at least a single physical backup is very important. If someone want to dig into the chain, then I have a similar puzzle, good luck finding it:

1. The amount was exactly 10k satoshis.
2. It was sent from this site as a giveaway, for writing an email: https://web.archive.org/web/20150106042627/http://99bitcoins.com:80/get-your-first-bitcoin/
3. I put that into this scammy wallet, probably in 2015: https://bitcointalk.org/index.php?topic=943146.0

I guess this was the first time, when I saw some on-chain transaction, filled with the data I wanted to use. Of course, those coins are now gone, and that website is no longer reachable (also because Tor moved into new address types). Probably those coins were moved long time ago, but no matter how hard I tried, it is impossible for me, to find them. Also, the mailbox, which I used, was removed in 2016, so it is long gone.

Quote

I'm guessing the most plausible things you can remember here would be the amount and a more accurate time of transaction, this ca narrow down the search a lot further.

I don't think so. If I am wrong, then tell me: which address I put in my email then, in 2015, when I received my 10k sats?

Quote

But puzzles that I can't solve are frustrating, until someone else solves them.

There are many unsolved puzzles, related to brainwallets, for example bc1qt2mdkehmphggajer3ur3g8l754scj4fdrmw3rn now contains 0.01 BTC. I guess it is related into writing "pi" value somehow, but the most obvious things, like writing "3.14" in ECDSA, does not lead to the right key (and addresses like 17mKugcBDEJbu391Fq41AdwLeGHwJLPRDf were cleared long time ago).