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The first capture of the then official Action Half Life/AHL website (ahl.action-web.net - later on ahl.telefragged.com [that logo looks familiar :)]) that can be found on the https://web.archive.org/ is from the 10th of October 1999 ( https://web.archive.org/web/19991010222710/https://ahl.action-web.net/ ), and the first entry on that page is from the 17th of February that year, which talks about the Beta 3 version:
[...] "on to the news: There is no news. Beta 3 will be comming 'REAL SOON NOW' aka 'WHEN IT'S DONE'. I really couldn't say more than that. It's pretty stable at this point. Some annoying bugs here and there."
[...] "You will see AHL beta 3 soon. And eventually v1.0 as well."
(The https://web.archive.org/web/20000818061941fw_/http://ahl.action-web.net/pre_august_news.shtml at the bottom of the page seems to lead to earlier entries, but the WayBackMachine's earliest snapshot of that link is from 2002.)
Although February 17th 1999 is the earliest date I can find that shows activity on the mod, the mod likely already started being developed in late 1998, directly after the release of Half-Life.
The first publicly available release, however, seems to have been on the 16th of March:
"Hey Action fans. Tonights treat will certainly make you spasm. hehe
The time has finally arrived, I bring you:
Action Half-Life!
Yes, Tonight at 8 pm EST (for europeans: thursday morning 1am GMT) I will start the release party on chat.planetquake.com channel #actionhalflife. At that time I will release the last trailer, and an hour later, you will have Beta 3!
Let the games begin!"
Although this is again about the Beta 3 version, I presume this is considered to have been the official release of the mod.
A couple more useful (?) links:
The team behind AHL's https://www.moddb.com/mods/ahl-directors-cut :
https://ministryofaction.net/
An overview of the original mod:
https://web.archive.org/web/20110811061356fw_/http://ahl.telefragged.com/manual/index.html