Is there any way to pull my contacts from my iPhone prior to "Restore"?

Is there any way to pull my contacts from my iPhone prior to "Restore"? Phone was disabled due to multiple erroneous passcode entries -- even though I did not attempt to enter my Apple ID/passcode info at any time and have the current passcode (which should not require change). Apple support has instructed me that I need to erase my phone (which is not backed up).

[Re-Titled by Moderator]