You can get them with a Level 1 Character, if you’re lucky enough for Izual to drop them on the first kill. However, it’s highly unlikely. By the time you reach Izual, with a new Character, you’ll probably be between Level 4 - 6. (If not higher).
Um… NO, they can’t. (As @TGO stated). You can only get the Plan: Staff of Herding from Izual.
The same is true for the Plan: Reaper’s Wraps. You can only get those from Malthael.
For me, it was Chilltara. Izual gave me a little trouble, but still wasn’t more than a half hour of farming. To me, that’s accepable. Chiltara? There’s more going on than just spawn rate.
Personally, I don’t agree with making something that needlessly rare and making it a required part of progression (Altar of Rites). That’s just an artificial barrier to completion. Anyone can keep the items out of your hands if they move the decimal far enough. That way they can clap hands over ears and just keep repeating “It’s just RNG” to justify it.
Do I want it on the first try? No. Gamers these days just have no patience whatsoever. Keep farming and it’ll show. Every season there are these posts which make out like it’s been removed from the game. It hasn’t. They just want you chained to a specific section of the game for days on end; that’s all.
Welcome to modern gaming, where fun and challenge are sat in the nosebleed section and mindless repetition has the entire front row.
I’ve got 2 staffs in my NS stash. An Infernal Staff left over from long ago, and a regular one I farmed up back in S28 when they were still hiding the fact that the altar wasn’t coming to NS.
I’m probably not going to bother with it this season. It’s not until the 2nd from last node. I’ve got the “pets pickup trash” unlocked, and I’m going to go for the “extra progress orb” and not bother with any more than that.
I’m just doing enough to finish the season Journey and get the pets.
RNG is RNG. I haven’t even started farming the staff components (although I already found the Shinbone) since I’m stuck at an earlier step, the one requiring an ancient Puzzle Ring. Plenty of regular ones, not a single ancient one. Dozens of rerolls, burning through most of my mats, the game just says “eff you” and doesn’t give one.
The RNG is going to kill me.
I got really blessed by RNGeesus on Americas region - my first GR (after finally getting to lvl70, that is) dropped an ancient Puzzle Ring. And on EU region, my first guaranteed primal was a Puzzle Ring 
“Do I keep it? Do I salvage it? Do I open a Vault?” - the first option won.
I’ve got the Staff of Herding plans a bunch of times running Sprinter. Could be a good way to farm it, maybe you should try that.
(/s in case it’s not obvious, 50min per attempt 
)
I would use the primordial ashes to make an ancient one. Wish you best of luck… wish everybody best of luck of course.
Finally did get an ancient after many rerolls.
I really won’t be wasting scarse Ashes on a Puzzle Ring when I don’t even have enough to unlock the potion powers.
Congrats with the result. You’re already above 800 with both Inna and LoD Necro. Soon primals are gonna rain from the sky 
Lol, it’s a different struggle for everyone. For me it was RoRG. It refused to drop even after more than 25 act 1 caches. I preemptively farmed the staff, cause I decided to farm visions in the areas that you search for the ingredients.
Same here on a on bounty run. Real lucky first time I killed Izual.
Almost lost sanity trying to acquire rank 125 Whisper. Finally managed to squeeze one for the Altar.
Staff components almost collected, only Gibbering Gemstone left. Hopefully won’t take too long.
Then it’s just some shards and couple salvaged primals. Right now I’d welcome trash primals, not ones I’d rather keep like the last one, Trag’Oul chest piece.
People say this, but it usually takes me 3-4 weeks before I get the 7 necessary primals (6 for the altar, one to augment my main weapon). The odds of going that far before getting an ancient puzzle ring are almost nil.
It’s been different every season, but this time around the shinbone took me the most tries.
The rotten shroom 
is the new Chiltara!
Never had that much “fun” finding it (on Europe servers); would even say more painful than her imbecile brick ever was!
After ten runs, “the” room was there for the first time, but of course no formerly alive plant.
Started making dashes.
After 73 runs (!) the room had appeared exactly 8 times and the 
“ingreedient” was finally there…
Now “only” need to have a heartattack in HC going for a Rank 125 Whisper of Atonement and then the expiatory stick can be donated to the void table… 
I know you meant the Black Mushroom.
For clarification: The Rotten Mushroom can only be found during The Darkening of Tristram Event on Labyrinth Level 9. And it is always there… somewhere.
Okay good to know, I should have known better before listening to random person saying that in Chat as I’ve never got one from one before but others said they did.
Ye, ye, ye, I know, you wisenheimer. 
That is why everything in that post is “coded”…
In my non seasonal stash on the European servers I have a collection of some legacy pieces, e.g. the Nightmarish Staff of Herding that had to be crafted using a crafted Staff of Herding and a recipe you could buy from someone (forgot), the legacy Manticore that has two slots, the legacy Puzzle Ring that sometimes made a treasure goblin appear when you got hit (used it sometimes running GRs in public groups, long after it became legacy, just to see who falls for it ;-)) and maybe some more, forgot, and don’t wanna check now…
Just trying not to confuse any new players that might find these threads. 
Confusion, that is the thing that makes life interesting! 
Scientists seem to call it chaos theory…
Not when we have to explain to all the players posting Bug Reports why they aren’t bugs.
Of course, traffic has been slowing down recently. But, still… we don’t need to see someone posting that they farmed the “Rotten Mushroom” for 40 hours and it won’t drop.