varnish server-side caching

[[Digital^Dude] ®]

Hi guys,

I set up varnish 3.0.3 on my centos box. I have magento running on a
website. Once the website is opened, it browses rapidly. But every time a
new user lands on the website, it takes ages to load the first page. If
varnish does server-side caching, shouldn't it pick up the index page from
the cache and spit it out?

Please suggest what I can do to make the initial hit on the website as
speedy as the rest of the surfing hits.

--
Thanks.
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