There's a non-zero chance of generating a wallet that has already been generated

Yes, there is. Mathematically undeniable.

No, it won't happen. here's why:

Intro:

Every now and then we stumble upon a reddit post in r/Bitcoin in which someone asks for the chances of someone else randomly generating the same wallet as theirs, or any variation of this topic.
I know mine it won't be a once and for all post that forever settles the debate, but allow me to try to give you my perspective and convince you that humans are bad at big numbers:

A few facts (as of today):

-24 word bip39 seed has a total of 2,9*10^79 unique addresses (from now on referred to as the seed space)
-Age of the universe is 1,37*10^10 years
-Bitcoin network total hash-rate is 7,8*10^20 hash per second or better 2,45*10^28 hash per year (from now on referred to as the bitcoin supercomputer)

Experiment number 1:

now, lets calculate how many lifetimes of the universe it would take for 1Million bitcoin supercomputers to go through 0,000000000000000001% (or 10^-20) of the total seed space:

2,9*10^79 * 10^-20 / (1,37*10^10 * 10^6 * 2,45*10^28) = 8,6 *10^14 universes lifetimes :)

so basically, if every person who ever lived (~100Billion people) each produced 1 Billion wallets in their lifetime (meaning 1 wallet each 3 seconds for their 100 years lifetime) we would end up with 10^20 unique wallets, and it would take ~ 800'000'000'000'000 (8*10^14) times the life of the universe, using 1M bitcoin supercomputers to have 1 on 290'000'000'000'000'000'000'000'000'000'000'000'000'000'000'000'000'000'000'000 (1 in 2,9*10^59) chances to get a collision. give it or take.

for comparison, if earth were the only planet in the universe to host life, the chance of life in our universe would be 1 in ~2*10^23. Now picture that life in the universe would still be ~500'000'000'000'000'000'000'000'000'000'000'000 times more likely than the scenario depicted above.

Hopefully this gave you perspective on how bad we are at grasping the magnitude of big numbers, but if it didn't, here's a game i like to play.

Experiment number 2:

Again, 24 words bip39 seed has a total of 2,9*10^79 unique addresses, while the observable universe has roughly between 10⁷⁸ and 10⁸² atoms. Lets then say we consider the two numbers to be equal.

Now, here's the game:
I pick a random atom in the whole observable universe and then ask you to do the same. you win big time (i give you 1Billion $) if you can pick the same exact atom, if you can't you give me 100$. This might already give you an idea of the magnitude, but if you're not convinced and want to play nonetheless, I'll even allow you to continue picking atoms until you make it, does that seem fair to you?
So your chance now depends on how many attempts you can make per second and how likely you want to be to be correct. Lets say that you want to have 50% chance of picking my atom, then you'd need to go through 50% of the possibilities, that are (2.96/2)*10^79, roughly 1,48*10^79. Not very different i am afraid.

One of the best supercomputers out there is the bitcoin network, so now I even allow you to rely on that to make our atom picking faster, it can perform 7,8*10²⁰ operations per second, therefore--> 1.48*10⁷⁹ / 7,8*10²⁰ = 1,89*10⁵⁸ seconds would be required for you to pick half of the universe's atoms, roughly 6*10⁵⁰ years, 6*10⁴¹ billion years or 4,6*10⁴⁰ times the age of the universe.
All this time, with the most powerful computer network known to mankind, just to have a 50% chance. Now, imagine you had 1000 billions earth-like planets at your disposal, each with a bitcoin network super computer, and 1000 billions universes each with 1000 billions earth-like planet each with its own bitcoin computer, each searching for the same wallet (I mean atom! sorry), it would still take 6*10²⁷ billion years to, again, have a toss of a coin chances to get it right, so I want to be even more fair to you, and instead of 1 atom, i pick the equivalent of 100Billion people, each picking 1Billion atoms, therefore 10^20 wallets (atoms!), and you win if you can pick any of those.. it would still require 6*10^7 Billion years!

Would you still play with me?

(btw, there are only ~55Million addresses with balance in existence as of today)

tl;dr: the chance is virtually 0 in any universe, however you look at it, whatever you have at your disposal to perform the task.