A lot of anime I've seen don't have openings in the first episode, instead the openings start from the second episode. I cannot particularly name any of them besides Boku Dake ga Inai Machi.
Why do some anime not have openings in the first episode?
Several reasons: Production cost, first impression, spoilers.
Theme songs are commonly used to save money on production. Draw that opening once and show 90 seconds of a roughly 22-minute episode every time. And there is also an ending which is a double value :p
When a series is only starting, you might want to make it interesting right away, and not just show the opening that the devoted viewers are already used to, and won't switch the channel if they're not entertained enough by it.
If the opening animated sequence features content that might need at least some introduction and explanation, that is planned to happen in the first episode, it would be good to use those additional 90 seconds for a more natural development.
The anime Kotoura-san is like this as well. It starts off showing you a type of introduction. From my point of view I feel that animes do this in order to tell a story more thoroughly without the spoilers that most openings usually show.
That way you aren't introduced to certain characters too early and you gain a better understanding of what the anime is really about.
Plus by doing this one is able to fully appreciate what the anime is trying to express, while at the same time building suspense as well as creating more depth and appreciation to the overall series.
I value animes that truly put in the extra mile instead of taking up too much time with an opening theme.