After it becomes a creature, Mishra's Factory will still have all its abilities.

A noncreature permanent that becomes a creature can attack, and its abilities can be activated, only if its controller has continuously controlled that permanent since the beginning of their most recent turn. It doesn't matter how long the permanent has been a creature. Notably, if you turn Mishra's Factory into a creature on the turn it entered the battlefield, you won't be able to then activate its first or last abilities.