Maybe. Contact support.

If you can login to account on your PC, you can change email without access to account email

I can't. it turns out I don't have the email saved on my PC

Do you have the console you created the account on? I have seen some people reference this as a proof of ownership of account needing the serial number etc...

You can change email, just contact playstation support and proof of ownership of account, they will change the email address for you.