Sign in to Origin Account

I contacted support and the short answer is there isn't a way to simply log in.

My chat transcript:

Jon: Thanks for contacting EA Customer Experience, my name is Jon XXXX. How may I assist you today?
you: hi, i'm not sure how to sign into my origin account
you: every time i try to access online features, i'm prompted to create a new account
you: where do i go to sign in?
Jon: That would be frustrating but let me check on this. First may I ask for your first and last name as well as your PSN username?
you: XXXX XXXX
you: PSN user: XXXX
Jon: Thanks XXXX. Were you able to play before online without any issues?
you: i haven't tried before
you: when i first got the game i couldn't remember my origin password, so i skipped it
Jon: I see. You may just sign in to your Origin account to link your PSN ID to it and play online.
you: that idea crossed my mind, but when i tried that i wasn't sure where to go to link accounts
Jon: Logging in to your Origin account on your game will do that for you.
you: yeah, that's what i'm trying to do
you: but i can't find where i can simply log in
you: (only creating a new account seems to be the only option)
Jon: I see. Do you have any EA games demo on your account?
you: i'm not sure what you mean
you: i have had to use the origin account before
you: there is just nowhere to go in NHL 14 to log in
Jon: I understand but have you downloaded any EA games / EA sports demo on your account?
you: not that i recall
you: but my origin account is about 3 years old
you: so it's possible
Jon: Thanks. Can we try downloading one please? Once downloaded and once you launch the game you will be asked to login to an EA account. Logging in to the demo will link your PSN ID to the account and it should let you p[lay online.
you: so there is no way to log in when i'm just playing NHL 14?
Jon: Since you have skipped the first-time login process you can try this suggestion as a workaround.
you: i'll take that as a no
you: what a joke
you: thanks anyway
info: Your chat transcript will be sent to [edit: email address removed] at the end of your chat session.
Jon: I hope though that I was able to answer all of your questions for this contact. Would there be anything else that I can help you with?
you: you weren't, but that's because the game's menu organization sucks and obviously there is no easy way to log in
you: nope
you: bye
Jon: Should you have any other inquiries and concerns, please don't hesitate to contact us or visit help.ea.com. Thank you again for contacting EA.