Yeah, of course! Nothing changes about the average time needed to mine a block at a given hashrate, but it’s certainly possible to get an outlier.
It is also possible to find it after the double amount of that time. We may consider both occasions possible, but their “center” which comes more often than those two, is 4,722,366,482,869. That's the rule.
Of course I fully agree

It’s really very similar to lottery, where you’d on average need to play for multiple lifetimes to win it, yet people do win it from time to time.
Hmm, I wouldn't say that it's similar. Each person is allowed to buy as many tickets as they want, but they usually buy less than five and they never buy around half of the total tickets to maximize their chances. In Bitcoin, pools do so and you stand no chance on winning this “lottery” if they pass on you that far.
Specifically, three pools at the moment own 45.14% of the hashrate.
The existence of pools doesn’t change your previously mentioned number though does it? Even if theres more hashrate in a bunch of places and its not evenly distributed, the amount is still the same and shouldnt change the chances of solo miners.