In theory maple seed need 60 to 90 days warm and moist stratification, followed by 90 to 120 days of cool and moist stratification. BUT not all seed reads the books. What you do depends in part on how much seed you have. if you have a lot of seed, you can run several different experiments. If you only have 5 seeds you only have "one shot" at this.
Myself, I would store seed dry, in refrigerator, until July or so, then soak the seed overnight in water, then put seed in moist peat or coir based mix. I use plastic zip lock baggies. Leave them on your desk where you can glance at them daily. They should swell and send out a short tap root. Majority of seed will then pause waiting for cold cycle.
However in every batch of 1000 seeds some significant percentage, at least 1% to 5 % will go ahead and grow without any stratification. This is a "natural error" designed to help have some seedlings survive in case the weather is screwed up the next year. A similar percentage will not sprout until two cycles of warm and cold stratification, if they don't rot or get eaten by insects first.
So if a seedling or two send out more extensive root and begin to show the shoot that will become the trunk and leaves, take these out of the baggie and pot them up separately.
Allow the baggie with the dormant seed serve its warm dormant stratification on your desk top for 90 days, then move the bag to the refrigerator for the 120 days of cold dormancy. During the cold phase, especially as the end of the cold phase approaches, they will begin to grow even in the refrigerator. Growth will be slow. I find it better to just relax, and leave the sprouting seedlings in the baggies until after "last frost" danger has passed. Use a calendar, start with your average last frost date for your address. Work backwards to figure out when you should start the warm stratification.
An alternate, is just plant the seed in a flat in spring, put the flat outside in spring, keep moist all summer, leave out all winter. This way as seed germinate, they will be out in the sun. Only hazard is squirrels and other pests eating the seed on you before they sprout. I tie wire mesh down over the flats I sprout seed in to prevent vermin from digging in my seed flats. Using 1/4 inch hardware cloth allows the seedlings to come up through the wire. After leaves drop in autumn it is easy to lift off the mesh either end of first or second year. Even with pines, the will ease through the mesh when you lift the screen if you are gentle.
