Well, I must say that is pretty bizarre. On the MOM website it says that you do not need to login to check the status of an EP application but when you go to the check status screen it does indeed ask for an NRIC/FIN number. I can see how you would be stymied. This seems like a bug to me.
https://eponline.mom.gov.sg/epol/PEPOLE ... yAction.do
Since I have an NRIC number I will be happy to check for you, if you wish. You don't get much information... it will only say 'accepted', 'pending', 'rejected' with no additional information. So, your application would be pending if it is progressing normally or if they have asked for additional information via your local SG address or they are doing a deep dive on you.
When you do log in you get this screen (part of it).
MOM no longer sends letters to inform of the assigned FIN and/or application number (according to the website) so you will need to provide me with a passport number by the looks of things. I'd suggest email to me if you want to proceed.
MOM does not send approval notice for an Entrepass by email, nor does it use email to ask for additional information so make sure that your local SG address is correct and checked for mail once in a while.