It would be interesting to hear your actual analysis of why the showrunners decided to have the three made first instead of last. I've always thought that the reasons were fairly obvious. First, Season 1 needed a strong, climactic finale (as an aside, look at what happened with Season 2 of House of the Dragon, a series that shot itself in the foot by having a season finale where nothing much happened). This meant that we had to have some rings forged. But how to do this in the time available? If the seven or the nine were forged in Season 1, then we would have needed to introduce Dwarf Lords or Kings of Men, and we would have needed Sauron to be in the open, influencing Celebrimbor from the beginning. This would have not only negated the mystery surrounding Sauron but would also have shunted Galadriel and Elrond to the side- our main characters. Add to this, probably the vast majority of the viewers had not read the books in such depth; the three being made last is only mentioned in passing in several places if I remember correctly. However, most viewers will recall the verse, "Three rings for the Elven Kings...", and they may remember the prologue to Jackson's The Fellowship of the Ring, where Galadriel says "Three were given to the Elves...". So the solution was to have the three made without Sauron's direct involvement by having Galadriel out him as Halbrand before they could be forged, and to have Sauron return later and reveal himself to Celebrimbor in Season 2 as "Annatar", a bringer of gifts. We can still have Celebrimbor consider the three to be his greatest works- he may be somewhat frustrated at the beginning of Season 2 by not quite being able to match his accomplishment and thus needing some help...leaving him susceptible to Sauron's ultimate deception.
Note that this is my own analysis of why they decided to have the three forged first-- not saying that this was "right" or "wrong". But certainly this was not done because "the showrunners have no respect for Tolkien" or any such silly reasoning.