I think that with Petrie's birth it can go in different directions.
Perhaps they had included it originally in the film but had to cut it out as it was repetitive, what with four dinosaur births already in the film,and would thus have been boring for the audience to have to go through it again.
They may not have included it at all, as to give the element of novelty suprise in Petrie's character appearance. I mean, if there had been a birth scene of Petrie and we discovered early on that he couldn't fly, then that would have spoiled one of the important (in my opinion

) aspects of the film.
He may have been born before, but I don't think that is acutally so otherwise he might have been dead long before from predators etc.
However:
That just doesn't happen. Before a movie goes into production the script and the plot's final drafts are already finished, especialy in animation, you just don't throw in a character in the last minute.
Actually, there have been several cases in which an animated character survives pre-production; various story boards and drafts etc, then during the actual movie-making process, the character is dropped completely from the film. An example of this is from the The Lion King film, in which a fennec fox named Bhati was dropped (along with Mheetu; nala's brother-although I believe that he was dropped during pre-production at story board).
I don't believe that the animators placed Petrie in, as a last minute character. To be honest, animated film makers are generally quite organised, they may drop characters during story boards (like Mheetu for the TLK) or during the film makng process (like Bhati) but they, as far as I know, they don't add characters with the amount of personality and story line that Petrie has, into a film part way.