I think they wanted all the major characters introduced first.
The initial team we see is Professor X, Cyclops, Storm and Jean Grey. They are all big characters in the X-verse.
The first film introduces Wolverine and Rogue, both very important characters. We also see Iceman.
The second one introduces Nightcrawler, whose powers stand out amongst the rest.
The third one adRAB Beast and Angel, the last of the original x-men of the comics.
Gambit is a relatively new character to the X-Verse, from the 1990s I think. The producers and writers have just said that when they introduce Gambit, he won't be a side character. He will have a large introduction, just have patience!
Now, I'm sure I only just had a post like this in the X-Men thread

Did I really need to say all that^