A health card is not an acceptable form of id in ontario, so it won't help you anyways.
The only other thing i can think of is a byid card
http://www.lcbo.com/socialresponsibility/byidcard.shtml
or a passport would work too. It pretty much has to be government issued photo id.
Go get your g1 and if you have a legal id with a picture you can use to two in conjunction with the docs they give you while you wait for your card to come in the mail. A citizenship card may work as well - or a native status card
Good luck!