It's your landlords responsibility to take care of it, by hiring a Exterminator, but sometimes their products don't work that well.
This is the nuclear option. We used it after countless times getting the exterminator in and it not working. haven't come back in years: YRMV tho. Advion
Advion worked really well for a relative.
The pucks:
https://www.amazon.com/advion-68663-Arena-Cockroach-Station/dp/B08HWHD58L
or the gel for inside counters, etc. (don't put it anywhere the baby could get to it)
https://www.amazon.com/advion-Plungers-Cockroach-Insecticide-Australian/dp/B00730QW70
Use this:
advion 383920 4 Tubes and 4... https://www.amazon.com/dp/B00730QW70?ref=ppx_pop_mob_ap_share
https://www.amazon.com/Vendetta-Cockroach-4tubes-Roach-Killer/dp/B015BSUAZU/
I used to use Advion and some IGR discs but this seems to do it all in one product.
honestly, you cant eliminate the problem in the building but you can keep it out of your unit.
you usually want high knock down because it only kills the ones you see.
1) bifenethrin. mix as directed, spray perimeter, and all entry or access paths, one a week at first, then once a month. bifen is a low know down residual effect so they take it back to socialize and typhoid mary all their friends. keep pets away until dried, and I personally wouldnt spray in the pantry except around the floor perimeter and all the way around the doorway top to bottom.
https://smile.amazon.com/gp/product/B00ARKSC4E
2) advion cockroach bait gel in the cabinet hinges and nooks and crannies. they eat it, take it back to the nest, and they all die.
https://smile.amazon.com/advion-Plungers-Cockroach-Insecticide-Australian/dp/B00730QW70
3) advion ant bait. they say it works even better than bifen. but bifen is so cheap, I say do both.
https://www.amazon.com/Advion-Ant-Bait-Stations-Bag/dp/B004HD973W
I've used this stuff before:
https://www.amazon.com/advion-Plungers-Cockroach-Insecticide-Australian/dp/B00730QW70/
https://www.amazon.com/Advion-Cockroach-Tubes-Control-Syngenta/dp/B0148W0WOE/
Its probably the only thing I've ever used that decimated roaches and I would say I had a similar infestation level as you did. It was also apartment style but managed to do the job regardless of neighbor cleanliness.
For bugs order Advio from Amazon it works. Then get the Gentrol to cripple the bugs from replicating. It's expensive but it works. Seal all cracks and fill holes if you can. Stop all leaks of water. Here's the link to the pest control https://www.amazon.com/advion-Plungers-Cockroach-Insecticide-Australian/dp/B00730QW70