There are not many options to speed things up in the beginning of the game. The length of time a pregnancy lasts depends upon the game speed setting (from about 20 minutes to over an hour), but you can sometimes speed up the birth of babies by using growth hormone. That's not a very good idea for the less valuable common fish, though, because the growth hormone is expensive.

Some people set their system clock ahead, but that can mess up other applications (and kill your fish, if you're not careful).