I'm not sure what you mean by the 3 months comment.
Your current WIN card has probably expired, go to AlbertaRELM, renew it and change your address to your new Alberta one as your primary residence.
Far as I know there is no wait period now once you claim Alberta residence status and you can go hunt by yourself without any guide requirement.
Once you renew your WIN card online it is immediately active and can be used right now to apply for special hunting draws.
Timeline to apply for special license draws ends at midnight June 23, so if you hurry you can get in on them.
Without studying a bit you may not know what/where to apply for, so be it, just put in an application for every draw you can and 999 each application.
You will gain a priority point of 1 for draws by doing that before June 23 and earn a year right now.
Hunt this year with over the counter general licenses that don't require being drawn for a special license.
New Win card-$8
Wildlife certificate-$28.22
Draw applications-$3.68 each
https://www.albertarelm.com/cust.faq.page#cards
https://albertaregulations.ca/