A number of people who haven't run into sampling before often intuitively think that a sample size needs to be some given proportion of the population size, but it does not.

Sampling doesn't work by relying on checking a large proportion of a population and relying on the fact that it's impossible for the sample to deviate by more than a given amount from the population, since so much of the population has been covered.

Sampling works by relying on the fact that it becomes extremely statistically unlikely for a randomly-chosen sample to deviate dramatically from the larger population once one reaches a (relatively small) number of absolute samples. Most sample sizes you'll see in random polling or similar are maybe 1k or 2k. Doesn't matter what the population size is (or, it does matter a tiny bit, but the benefit of covering a large portion of the population becomes extremely small very quickly as one's sample size grows).

https://en.wikipedia.org/wiki/Sampling_(statistics)

To put it this way, say you had an Olympic swimming pool full of randomly-mixed red and yellow jellybeans. If you picked 100 with your eyes shut, and none of them were red, you could say that it's very unlikely that there are very many red jellybeans in the pool. That would be true regardless of whether you had one Olympic swimming pool or whether you had so many pools that you had a whole ocean of jellybeans.

Sampling doesn't provide a hard guarantee, but probabilistic ones. Yes, technically, it's possible for you to get 100 yellows in a row, even if the the pool is 50% red and 50% yellow. But the chance of that happening would only be about 0.5¹⁰⁰, or 1 in 1,267,650,600,228,229,401,496,703,205,376; staggeringly unlikely.

If you picked a thousand jellybeans at random, and got 1000 yellows, it'd be about 1 in 10,715,086,071,862,673,209,484,250,490,600,018,105,614,048,117,055,336,074,437,503,883,703,510,511,249,361,224,931,983,788,156,958,581,275,946,729,175,531,468,251,871,452,856,923,140,435,984,577,574,698,574,803,934,567,774,824,230,985,421,074,605,062,371,141,877,954,182,153,046,474,983,581,941,267,398,767,559,165,543,946,077,062,914,571,196,477,686,542,167,660,429,831,652,624,386,837,205,668,069,376. If your Threadiverse client truncates this, it's 302 digits long.

That's true even though in both cases, the jellybeans you picked, the sample size, is a vanishingly tiny proportion of the total jellybeans in the pool, the population size.