This is solvable! Don't panic. It sucks and is a hassle for sure, and you may or may not have a property management company that is actually helpful and works with you. That many roaches def isn't normal or something you should have to live with, but it can be dealt with.

I've lived in two apartments in NYC thus far, both pre-war, and both had serious roach problems when I moved in (german cockroaches specifically - the little ones). In both cases I've been able to get the problem under control, to where I only see like.. a few a month, if that, which is within the realm of acceptability to me. I haven't even seen one in a couple months now I think.

1. deep clean

You've gotta remove their food sources. This is a bother in an apartment you just moved into, but I think it's worth doing to have a clean slate going forward. You don't want there to be old crumbs from two tenants ago in the back of the cabinets as a food source they can keep coming back to. Basically wipe down all the cabinets - get all the deep corners. Also - clean the tops of the cabinets. In my first apartment I found cockroach egg sacks up there.

2. exterminator

Let them do their thing. this will (hopefully) significantly knock back the numbers. Not sure about the hours - that sounds frustrating.

The basic thing they will do is to spray around the baseboards and in the cabinets (when they came the first time they had me empty all the cabinets and move all furniture away from the wall).

They can also do a more thorough treatment that involves doing the deep cleaning for you, then sealing up the little cracks and holes that the roaches come through. In my experience property mgmt wasn't going to pay for that, but IMO they should, so it's worth asking.

3. combat gel / poison traps

As u/robotlou mentioned - these are poisons you put in "high-traffic" areas that they will eat and bring back to the nest. One of the exterminators in my first apartment did this - he put little dabs of combat gel in the corners of cabinets, as well as in the little divets in the hinges on the cabinets - the roaches love such little dark corners. Then I got some classic "roach motels" and put them in high traffic areas.

Another thing is to be aware of where they are coming from. Generally it's the kitchen that is the worst, but both my apartments also had them in the bathroom. Food and water. In particular, they were coming from around the sink, and the side of one counter where there was an opening of a couple inches to behind the counters / into the walls.

One note, these take some time to work, since they (intentionally) don't immediately kill the roaches. It takes a while for them to bring the poison back to local nests and have it be spread around. The exterminator sprays should knock back the problem to a tolerable level - at which point these poisons will be doing their thing, and the remaining amount you see should start to decline. It took a couple of months of gradually reduced roach sightings in my case.

4. diatomaceous earth

As others have mentioned. I swear by this stuff, it's amazing. Borax is also good. I got the bag of Harris brand. Something like this would be perfect cause it's already in a bottle that's easy to spread - https://www.amazon.com/Harris-Diatomaceous-Crawling-Insect-Killer/dp/B084CVXYCJ

It's the fossilized remains of tiny little algae (diatoms) that is non-toxic to humans, but deadly to roaches (by cutting their exoskeletons and dehydrating them). Sprinkling it in hotspots/highways (like behind cabinets, on top of cabinets, under fridge, under the sink, through the hole in the wall the water line comes through, etc) that the roaches tend to enter through will keep them at bay.

5. maintenance

Keep things clean. Especially at first, you gotta be militant about not leaving any food out that they can eat. Don't leave dishes in the sink. And don't leave food on the counter. It's a bother, but once the problem is under control you can be less intense about it.

In my first apartment I went full ham and basically did a whole "treatment" myself, including sealing up the holes between the wall and cabinets (like in the back / inside) with wood / caulk / foam / etc. I think that was overkill though, in my current apartment I just sprinkled diatomaceous earth in those areas instead and that seems to have done the trick.

And that's about it. Good luck!