That's a pretty interesting question. For background, we should let
other readers know that you're wondering about how big the universe was
shortly after the Big Bang
The universe has been expanding since the Big Bang, but there's now
very strong evidence that the initial expansion had an extremely brief
period of extremely rapidly increasing expansion, called inflation.
If by 'universe' you mean all the stuff that makes up the visible
universe, its radius after initial inflation was (very roughly) 10 cm,
the size of your fist if we understand this site
correctly. That's to be compared with 14 billion light years now. If by
'universe' you mean 'everything', including the stuff beyond our
current horizon, we can't answer, because we don't know if we're part
of a finite universe or an infinite universe.
By the way, it seems that the universe is again in a period of inflation, although this time it's not very dramatic.
Here's a nice Website discussing these questions in more depth
-Mike and Tamara
(published on 10/22/2007)