The NVC doesn't "approve" it. It is already approved by USCIS when it is sent to the NVC and they hold it until a visa is available. There are different waits depending on what country you are from. You have to wait until your priority date which is usually the date your I-130 was approved. You can check the visa bulletin for thd priority date they are currently processing. You will be in category family 2A. Currently the wait is about 4 years and 5 if you are from Mexico. If your mom Naturalizes you can move into F1 category which is a few years shorter.
If you get married before your mom Naturalizes you will lose your priority date and have to start over.
Current Visa Bulletin-
You may call me for a free consultation at 206-724-1940.
Andre Olivie, Esq.
I agree with the above. If the priority date is current or close, once the NVC gets all the paperwork it needs, it should forward the case to the consulate within 3 months.