My usual trick is: Tell the robot you need status on your green card application. It'll ask you some questions, along the lines of "did you do these steps you were supposed to do". You have to answer correctly. I forget what all of them were, but just think logically: answer that you don't have an online account, you didn't receive a receipt notice, it's been more than 90 days, etc. Any question it asks you, just the outcome that would logically mean that you need to talk to an actual person.
After you get someone on the line, you get into hard mode. A lot of times this person will tell you that "this is the way it is" in terms of not having a response to your application yet. Sometimes it is indeed the situation that you have to wait, but sometimes these Level 1 call center folks don't know any better and you should try to prod them to see if you can get them to escalate the case to Level 2 where they are more clued into where the delays are and if they're legitimate or if your case is getting lost in the shuffle.