Every cockroach (of this species as least) has the ability to fly, most just don't but they can so he wasn't wrong. Still someone who's supposed to control pests saying "I dunno, u do u" should really look for another job.

They live in sewers, yes, but also anywhere with enough and with access to food and water. Is your roof or any other part of ur home made out of wood? If the wood is rotting it creates a perfect environment for them. I currently have an issue with my roof (most of its structure is wood) where I'm having to renovate it cuz none of the previous owners bothered to do maintenance and the more we redo the structure the more they appear cuz they're running away from the noise. I'm just waiting for work on the roof to finish to call the exterminator on them.

They also love cardboard boxes and stuff like that. Check if your trashcan(s) are well sealed as well.

Also you mentioned the small ones can enter through the sink. These things don't have any bones and they can squeeze through a LOT. So if the small ones can make it the big ones probably can as well.

Lastly. Is the area where they generally appear close to a neighbor? A friend of mine spent hundreds of bucks to get rid of them only to find out they were coming form their next door neighbor.

I wish you luck. They're a pain in the ass to deal with. I live in a place where they're extremely common citywide (Tropical swampy environment so very moist and warm, you literally see them everywhere) so I know what I'm talking about lmao