I'm planning on building a deck with Pandemonium, but I'm unsure about trigger timing. Will Pandemonium trigger when I play a creature with bloodthirst and give it the counters after it resolves?

Your question seems to be two in one. The first part is answered with a Yes, the creature will trigger Pandemonium. The second part is No. Bloodthirst alters how the creature enters the battlefield by placing counters on it if an opponent has been dealt damage before it starts entering the battlefield. If the opponent hasn't been damaged before it enters the battlefield then bloodthirst does nothing, even if that creature entering the battlefield triggers a damage ability that can target a player.

If, on the other hand, the damage happens because you cast the creature spell, then bloodthirst would apply. Like with Leyline of Lightning.

technically, in that example, the damage is happening after you cast it but before it resolves. this distinction can matter at times.

but yeah in the case of pandemonium, Bloodthirst doesn't work. Bloodthirst isn't a triggered ability, it's a replacement effect that modifies how the creature enters the battlefield, so you can't stack it with triggers to get the effect you want.

However, these responses don't mean the deck isn't viable.

For example, long ago I used Shrieking Drake as a Pandemonium engine (Cast, Trigger, Drake returns itself) in Type 2 (tells you how long ago that was). Similarly, if you have a cheap bounce creature or token generator, you use that once each turn and each Bloodthirst creature thereafter will meet the requirements.

"viable" is probably stretching it, but sure, you can trigger Pandemonium with a separate thing, then after it deals damage play a Bloodthirst creature with its bonus counters. in that way, Pandemonium behaves exactly like any other source of damage. but as Edacade points out, if you want Bloodthirst creatures to supply themselves, your easiest tool is probably leyline of lightning.

Viable, from a casual deck theme standpoint. Leyline of Lightning is indeed another option (among many other options) and it really just depends on the rest of the deck.

Yeah, I realize the question was worded a bit strangely now, I was tired when I wrote it so I didn't know how to put it into words lol. But I got the answer I was looking for anyway, thanks. Actually my deck idea wasn't around bloodthirst itself, more Pandemonium and Rakdos, Lord of Riots, and the bloodthirst creatures I was hoping would combo with Pandemonium to give them the counters after it deals damage to the opponent after I cast them, and said damage would also activate Rakdos' mana cost reducing ability. In any case, apparently it won't work so it's a moot point, but I won't get into the deck here since this isn't the correct place for it.