Only way is through Hans. I don't know if Jagex keeps record of the exact timestamp, but there's no way to check if they do, so the day is the most precise you can get.
You can use some online count-back-x-amount-of-days-calculator-website to figure out the date from the amount of days Hans gives you.The Wiki needs a hand, and Bwian's will gladly take the rest of your (carcinogenic) body!
The Answer to the Great Question of Life, the Universe and Everything is...
Eat A Wsaid: Matmano9said: You can check the 1st email you linked to your account.
Search for "Jagex"or "Runescape"
This may help, otherwise. Hans is your only choice
This would be helpful if I didn't have one of those Chad "log in with a userrname" accounts.
But thank you for clarifying. I was kinda searching the main page hoping a little bit. That's why he says "linked" because the email you use to login with on a new account is never registered as your contact email. And you were able to register your contact email with RuneScape way back in the beginning.