I searched for hybrid oaks, and I found this. I figured hybrids were more likely to have unusual traits, like early fruit; so, that's why I did the search.
Anyway, the link talks about how some hybrid oaks may express hybrid vigor, which means faster growth, which may mean faster acorns. Not all hybrid oaks express this vigor. Apparently, according to the link, it's possible to get acorns after only a few years. It says six years is typical for a hybrid in Michigan. There are some at the nurseries that say they mature in five.
You might check out the Instant Oaks first (some of them that they sell already had acorns last year), although it looks like those are out of stock. The other hybrids are generally 4-8 years from seedling to fruit.
Here's a link to the nursery that sells these hybrid oaks in Michigan. Request the desktop version of the site if you're on a mobile device.
Here's a Canadian nursery with a similar claim.
Here's another Canadian nursery with hybrid oaks.
If you're wanting to grow the acorns for deer, check out this forum thread. They offer some faster alternatives to oaks, and express doubt that the hybrid oaks will produce in the stated time unless they have ideal nursery conditions.
Another idea that might be easier than transplanting a mature tree is getting land with a mature oak tree already on it. That might sound a little drastic, though—
I'd investigate the hybrids. They sound like they're exactly what you want. I would personally recommend getting several kinds instead of just one (that way, you might find the perfect one for your soil and climate).