How long does nearsighted person usually go without needing glasses for driving test?

Depends: It all depends on your visual acuity test at the dmv. If you score low enough, the dmv will require that you get glasses/contacts before being issued a license and it will be marked on your license that you are required to wear corrective lenses whenever driving.

State limits: States have a visual acuity limit below which glasses or contacts are a requirement. This is usually 20/40 in most states. You will be required to have corrected vision better than this to get an unrestricted drivers license. Most states mark on the license the need for glasses and you better have them on if you are stopped for a traffic incident.