Hi all… i found the best way!!!
Use Kanai Cube - Reforge Legendary
If you have been farming normal Puzzle rings, or have a few… do this!
I got my ancient on first roll!!
Otherwise…i think much harder to get 2 Primals to salvage and cube…
And grinding GRs wont help much, except if you are lucky to get primals…but if you end up with a few normal puzzles, go Reforge!
Good luck!!
Sure. Luck is the best way.
Do GRs or bounties to get the ring.
If not ancient, use reforge legendary.
Took me 2 tries.
I would not recommend upgrade, primals are hard to come by and you’ll need several eventually for the 3 bottom nodes on the tree.
I totally lucked out and reforged a regular and got an ancient on the first reforge. RNG smiled on me that day. Sadly, that’s the only time 
Just throwing it out there that Primal items from crafted sets like Aughild or Guardian salvage into primordial ashes. You can do probably ten rounds of T16 bounties in two hours in a split public game. That’s 100 caches yielding up to 400 legendaries on their own, a bunch of blood shards, and 440 of each special crafting material, which let you craft at least another 880 legendary items (Veiled Crystals not withstanding) for ~3 primals on average. There’s your fake primal ancient puzzle ring.
This thing was brutal for me to acquire. I finally decided to craft one at around paragon 950 after finding 20+ puzzle rings, reforging a dozen puzzle rings, and upgrading hundreds of rares. This is after I had already opened up all the altar of rites seals requiring ashes. It was incredibly infuriating because in that time I had found 3 ancient bovine bardiches and a primal bovine bardiche! Ugh. Hopefully you’ll have better luck than me. Now I’m stuck on the gibbering gemstone. These are not fun roadblocks, imo.
I had collected about 10 rings, all were normal. I finally caved and used the reforge recipe. Got an ancient on the first attempt. Pretty much used up my luck for the week.
That said, I have completely finished all the seals. All I need now are some primals to salvage (that I’m willing to salvage). lol