Is there any other way to get the Strange Alien Artifact besides Chridrens toys, Negotiate Additional Delivery of Rare Commodities assignments and buying one on the exchange?

Nope...

Thoose are the only ways...

There were some in random Grab-bags recently, but I don't think that offer is still on.

A secondary track for getting Strange Alien Artifacts is through the various artifact hunting assignments, including "Recover Artifacts from...", "Collect Artifacts from...", "Salvage Artifacts from...", "Study Ruins on..." Very occasionally, critical success in these missions can result in a Strange Alien Artifact

He's right, on occasion certain science gathering Doff missions sometimes give one on a crit. Nice way to score a good 500k+, I have no faith in being able to make a console so I just sell the artifacts.

I think you can get them from Duty Officer packs as well. Not sure if that's still running.

I get these power them up and put them on the exchange. Don't see the point in doing the DOFF mission and risking my profit margins. I don't care what the rules of acquisition say...

I have 8 characters and i power them up from the NADORC assignment and then flog the powered ones, its so random i n what you get , most of the time you make a loss

I do the Dil mining event on 4 of them - when suitable - everyday alternating so i get 2 runs each character in the hour by doing the mission back to back and i can get around 60 rare traces each hourly run - i use the Rare Astrometrics Doffs which give a 60% chance to get more traces (best 200k per character i have spent for a while lol)

It's also worth mentioning that these can give you the rare traces needed to power the artifact.

Also the Scanning missions give the traces on a crit - you can easily get 20%+ chance, just do a lil tour around and pick up bucket loads - great for doing the Science section xp - some as quick as 30-45minutes

Didnt know the dilithium mines give anything but dilithium? You get traces as well? Havent done this for a while but there must have been changes since all they give at first was just ore dil

If you get

735 points you get 200dil (300 during the event)
775 points you get 200dil and 1 rare trace and a couple of common ones) (300dil during the event)

thats per node, i just got 12,000 dil and 63 rare traces just then by doing the mining event which just finished doing the event on 4 characters twice using the new Astrometrics Scientist (the rare +60% one)