Depends on your definition of "ignoring her" and still being able to play the game.
If you try to ignore Paimon right from the start then your best bet is to never approach her as she is waiting near the lake where you find the first statue of the Seven.
This... causes quite a bit of issues.
- since you never interacted with the statue, you will never get Anemo. Meaning you won't have any elemental skill / burst on the main character. You probably could use wishes to get other characters, but .... we will talk about that in a bit.
- the main quest won't progress, so you never meet Amber. Meaning no glider.
- other world quest elements seems to be stuck also. For example some claim that the shop in Mondstad are stuck in a "we are about to open" limbo forever.
- also, most of the other quests either have a minimum prerequisite advancement in the Archeon main story OR an AR requirement. So, you can't play most of them.
- you could think to outsmart the game by exploring and collecting chests to raise your AR.... but apparently the map is also stuck until you advance the story. This means that the red barrier is at full power, and you can't even explore the full Mondstadt region.
- your low AR will keep you out of most events and free giveouts, so your free primogems income won't be that much. You probably could still buy stuff with real money.. but it is really worth to spend on a butchered game?
Also, even if you somehow managed to find a way to workaround all of this (bugs? I doubt there is a way to go past the map borders but again the Dokodemo Door in Liyue apparently survived for a few patches...) I once again wonder what "ignore Paimon" means. I suspect that she would still talk to you if you crossed some trigger areas where she comments on landmarks and/or nearby zones, she would still comment on random event quests (like Pallad, assuming those will trigger in the first place since you never really started the main quest line), and she may even automatically start a dialogue upon entering the game when some events are running if your AR was high enough. Maybe you could skip those by trying to keep you AR low, but in that case probably you won't be able to really "play" the game.
Also worth noticing that on a pure "Lore" level, Paimon seems to be fully aware of the actual player playing the game since she directly speaks at you in the setting menu (Which not so randomly is called "Paimon Menu"). So, you could say that you are interacting with her whenever you start the game in the first place.
Anyway, if you are curious, this Youtube serie tried to do that.
No Element Traveler - Playing Genshin Impact without Elements