It appears based on the background of the VCs currently, you need to build a product/business, grow it, sell or do an IPO (returning a tidy profit to the VCs that funded you), and then join a firm after 'retiring.'
Yes, one way to get a job at a VC firm is to either be a successful entrepreneur, or have domain expertise that the firm needs. These include: (1) technical expertise - do you know a relevant technology inside and out (e.g. for biotech - do you have a PhD or MD)? can you vet potential investments? (2) finance - have you worked in investment banking before? helped raise money? structured deals? (3) do you have an outstanding network that you can source deals from? can you make sure the firm knows all the up and coming start-ups?
VC jobs are tough to get, even at the associate level (entry level). Typically firms are looking for some domain expertise they need. It can vary a lot. Background that include finance or consulting can be helpful, but aren't guaranteed to get you in the door.
At the higher (leadership) end of the VC job spectrum, it often comes down to "can you raise money?". Do you already have a track record of success?
I've seen there are two (highly generalizing) tracks:
1. Professional Finance/Banker types. Usually MBA track with some Goldman-Sachs-type experience.
2. Founders and entrepreneurs aka "Operators" who move into VC from an exit.
(Again with the generalizing) The former (MBA) tend to work later stage, whereas the latter (Founders) usually work early stage.
Late stage has more financial metrics and needs stronger traditional finance networks. This suits a professional finance type better.
Early stage requires a grass-roots network and some technical/operational chops can be a big advantage. Founders can also differentiate here as they can roll their sleeves up and help hands-on in more areas.
A less common way is to build up to VC as an Angel investor or some type of advisor. After getting a bit of a portfolio you can start raising a fund (or more likely, help someone else raise one and jump on). However, they tend to be founders with some level of liquidity. But if you're in for a long haul that seems to work too.