Yes, any homeowner or builder is allowed to submit the application and manage the build without being a LEED AP (Accredited Professional), or even having a LEED AP on your design team. You could receive a point towards certification by having an AP on your design team, but it isn't mandatory. Here is a page to get you started -
What you need to do first is contact a LEED provider in your region, it is with them that you will make your submission and they will perform a preliminary rating to see if how your design would score. This step allows you to see where your design falls on the point scale, and to see if changes are necessary to help you meet your own targeted goal.
Below are some pages that may be of value depending on how familiar you already are with the rating system. We built the first LEED v4 Platinum house in Canada a few years ago (linked below); in there you can find your way to the video guide we created following its construction, that may be of value to you as well. Also check out the following pages, best of luck!
If you see models you like, there is a sign up list on that page you can get on to get in the queue for delivery. We have very high demand at the moment so it’s hard to know exactly when we will be able to deliver, but we are coming online with new manufacturers and models soon, and for all across Canada. How soon are you building?