I absolutely fell in love with these in Miami. Love the fruit and the tree. I just plant them in a well-draining soil. You can start them in a smallish pot just be sure to pot up once they start to grow. They are EASY to sprout. NO, they will not survive 7a outside--no way! But they are very tolerant as indoor plants in the winter. Pouteria zapota a.k.a. Mamey zapota.

NJoasis is correct. Mamey is very, very tropical. I have both mamey and sapote, the sapote can tolerate a light frost, mamey will do nothing of the sort. The seed you have is of a fruit so sweet and apricot/almond tasting, I do hope it lives for you. What a mouthwatering fruit!
It's mother is a huge tree when full grown, I'd think you'd have to almost go 'bonsai' with it to have any luck container growing it. The bark is beautiful and a hardwood sometimes used for furniture. Worth trying for sure.
I have had some luck in actually cutting the taproot in these types of trees, and trimming rootball and the top of tree yearly (fall) in order to keep it smaller and therefore container grown. Maybe you could do that too, as NJoasis suggests
edit: When cutting taproot, if the plant survives it, it is from much love with soil food (not ferts, plant food) and lots of water until/if it recovers. The plant then sprouts many side roots, instead of the taproot. If it makes it, the plant really does thrive, and grows a rootball clump of large, vigorous roots. As odds, 1 in 3 make this transition.
Maybe it's all in the genetics of the original seed. Please let us know what happens with yours. This plant only throws fruit every few years, not annually like others, so it would be interesting to hear what happens with yours in zone 7 .
Read what 'soaht' has to say about rooting them up here:
http://forums.gardenweb.com/forums/load/tropicalfruits/msg0421151717141.html?18

This post was edited by MsMorningSong on Sun, Oct 13, 13 at 6:37

Yeah, look at the link that MMS referred you to. Just to give you a primer on how I got mine going: I used the damp paper towel method to get mine sprouted, then I just laid the seed on it's side with the taproot (peaking out) slightly into the soil. The taproot came out of the end that does not have little dark spot on the light colored strip. I didn't have time to get a good pot together so I just put them in what I had laying around. After about 3 weeks the seed split in half and opened up like a little dinosaur mouth. I don't have a photo of the sprout, but it is thick and tall kind of like an avocado. I put one in a 4" pot which is way way too small. I need to move it over. According to Seng, the growth rate slows down after the initial surge of growth.

Here are a couple photos of my recent sprouts:

Beautiful to see!

Here is one today (about 8 weeks old.) I moved it into a larger pot and put it closer to the window. Right now it is about 10-12 inches.

I have a black sapote in ground. About 6' plus. Several flowerings. No fruit set. Still too young. But I'm sure mine is grafted and I think the other sapotes also. So my guess is not to expect fruit. Unless yours will be root stock for future grafts. Maybe you could vacation in South Florida during the new flush season and make a graft? Good luck.

It's really a nice sapling. Mine grew into a curl, and was so pretty. I mean the base of the trunk. Yours looks so healthy! Good luck with it, I can almost taste the fruit just looking at the leaves :)