what is the fastest free way to get at least 1 satoshi I know CPU mining uses more power than its worth.  I know GPU mining uses more power than its worth.  Yadda yadda.  Regardless, I have a spare server, my home internet is on an unlimited plan, and electricity is included in my rent, so...

As a learning exercise, I have been running headless bitcoind for several weeks.  I have also run it on testnet3 at times, and used online testnet3 BTC faucets to get testnet3 BTC to my bitcoin-core testnet3 wallet.  I have also played with the command line RPC interface for querying the blockchain, the wallet, etc.

Now I would like to do similar with (non-testnet3) BTC.

However the faucet I tried is "giving" me like 23 Satoshi (within their internal account register) per captcha, with 1 h wait for next try, and 30,000 Satoshi payout limit, and 3,000 withdraw fee.  This will take 54 d if I visit it every hour 24x7.

And with the mining pool I tried (slushpool with bfgminer compiled from source with CPU, GPU mining enabled), I don't entirely understand the pool's nor miner's interface.  The miner claims to be working at 6 Mhash/s, while the pool at first seemed to be saying 0 hash/s.  But after 24 h, it seems to show 1 blip in its graph where there was momentarily 1 active worker, and the hash rate blipped up to 427 Mhash/s and then decayed back to 0 over about 1 h.  I suppose this represents the completion of 1 share but I don't see a way to set a lower difficulty than the default 128 (and haven't read enough about pools and shares yet to understand how that would help anyway).  The pool has a minimum payout of 0.1 BTC and thus estimates my time to next payout at 48 y.

What other free method can I use to get at least 1 Satoshi into my wallet sooner than the above?  Are there faucets or pools or other methods that are several orders of magnitude faster than this, such that I could complete my experiment in a day or two?

Note, please exclude answers that boil down to "mine altcoin and convert to BTC".  Also I've implied in my question (in addition to my hardware, electricity, and bandwidth being considered free) that my time, by mentioning faucets which mostly have captchas, is free.  However let's not extend that to "design a web site and charge in BTC".  And obviously not "buy BTC on exchange" as that is not free.  Also I don't mind if the transaction fee is exorbitant, e.g. I do the captcha equivalent of 2 Satoshi and only get 1 Satoshi.
There are no shortcuts, nor any free rides.

First off, you aren't going to be able to do anything with 1 satoshi.  You wouldn't be able to afford the mining fee to transfer it anywhere, which means that it has essentially been taken out of circulation.  As it stands, everything you can do with 1 satoshi you can currently do with 0 satoshi.  For amounts that small, you shouldn't bother.

Second, your time has value.  Regardless of your electricity costs, setting up a CPU/GPU to mine bitcoin will take time.  Furthermore, with so little hashing power, you aren't going to see a payout anytime soon...even while mining on a pool.  You are probably better off trying to use the faucet you mentioned.

As it stands, the least expensive (both time and money) and fastest way for you to obtain a usable amount of bitcoin is either to purchase some, or sell a product/service in exchange for some.

I know this is not what you are looking for, but I assure you that it is the truth.