What you are looking for is a way of warming up the cache. You could use varnishreplay
or a Web crawler, such as Wget or HTTrack to go through your site. Alternatively if you have a sitemap of your pages you could use that as a starting point and warm up the cache by looping over it and issuing requests on the pages using e.g. curl or wget.
Using varnishreplay requires you to first run varnishlog and gather a log of traffic before you can use it later for playing back the traffic and warming up the cache.
Wget, HTTrack etc. can be pointed to your home page and they will crawl their way through your site. Depending on the size and nature of your site this might not be practical though (for example if you use Ajax extensively).
Unless your pages take a very long time to load from the backend server (i.e. Apache), I wouldn't worry too much about warming up the cache. If the TTL for the cached content is high enough most of the visitors will only ever receive cached content anyway.