Advice for the Home Gardener from the Help Desk of the
UC Master Gardener Program of Contra Costa County
MGCC Help Desk Response: Thank you for contacting the UC Master Gardener Program Help Desk with a question about pruning your ginkho tree. Ginkgos (sometimes known as Maidenhair Tree) are an ancient tree from China related to conifers. They are long lived and generally do not need a lot of pruning. There are different varieties of ginkgos with different growth characteristics. For instance 'Autumn Gold' is an upright grower to 45', eventually spreading to 35' wide. 'Golden Colonnade' is narrow, at 45' tall and 25' wide. 'Presidential Gold' is broadly oval, reaching 50' tall and 40' wide. 'Saratoga' resembles 'Autumn Gold' with a distinct central leader. (This information is from the Sunset Western Garden Book.) If you know what variety you planted, that might help you understand your tree's growth pattern.
"Topping" is almost never a recommended tree pruning option, is rarely appropriate, and can be disastrous for the tree. Ginkgos are no exception and should have only one leading trunk from the bottom to the top. This means you should not shorten the tall growth, but rather leave it and wait for branches to grow from it. The best time to prune ginkgos is in late fall or winter during the dormant season. This link from SF Gate describes how to prune a ginkgo tree: https://homeguides.sfgate.com/prune-ginkgo-tree-20450.html.
Ginkgo are not usually bothered by insects or diseases, and are very tolerant of heat and alkaline soil. For more information about ginkgos: http://ipm.ucanr.edu/PMG/GARDEN/PLANTS/maidenhair.html.
I notice from your photo that your tree is still tied to its original stake. If the tree doesn't flop over when you carefully remove the, it would be best to remove the ties and that stake so the trunk can move a bit. That's how it will get stronger and be able to support the rest of the tree's growth. https://s3.wp.wsu.edu/uploads/sites/403/2015/03/staking.pdf
Please don't hesitate to contact us again if you have more questions.
Help Desk of the UC Master Gardener Program of Contra Costa County (SEH)
Note: UC Master Gardeners Program of Contra Costa's Help Desk is available almost year-round to answer your gardening questions. Except for a few holidays (e.g., last 2 weeks December), we're open every week, Monday through Thursday for walk-ins from 9:00 am to Noon at 2380 Bisso Lane, Concord, CA 94520. We can also be reached via telephone: (925) 608-6683, email: email@example.com, or on the web at http://ccmg.ucanr.edu/Ask_Us/. MGCC Blogs can be found at http://ccmg.ucanr.edu/HortCoCo/ You can also subscribe to the Blog (//ucanr.edu/blogs/CCMGBlog/)