Just an update on this:
My wife and I both applied for our OHIP and got it immediately. Our coverage started as soon as we go it. One tip is, if you are thinking of showing Utility bill or Bank statement as an address proof, it should be on an unopened Canadian post mail. You cannot download and print them out. This is applicable for new immigrants. In my case, I showed by phone bill on mobile app. Also, phone bill is the only digital proof of address accepted.