During Thor we see Thor talking (as a child) about how he wants to wage war on the Frost giants, like his father (Odin). So we know that the Tesseract must have been lost already.
Actually, what this shows us is that this is happening over a thousand years in the past.
- When Dr. Selvig is in the library, we see a book of Norse mythology. It has a picture of a full-grown Thor.
- Due to the mixture of real-world mythology, and the Marvel universe, the Asgardians were active on Earth about a thousand years ago, to jibe with our real-world history. It was during this time they lost the Tesseract on Earth during the war with the Frost Giants.
- This means that ~1000 years ago, Thor looked like a teenager or young human, at least. This is because ~1000 years ago the Norse peoples interacted with Thor, and passed around stories of him as a full-height person, not a short child. This then trickled down through time as Norse mythology
So in the scene with child Thor and child Loki, it's entirely possible that the Tesseract would be in the trophy room, since it hadn't yet been lost on Earth. However:
BUT, during Thor's coronation ceremony, we see some frost giants trying to steal the Tesseract from Odin's throne room (or wherever that was), even though we know that it was lost.
No, during this scene they attempt to steal the Casket of Ancient Winters. It's the device that allows the wielder to make blasts of severe cold. This is the device that later on Loki takes and uses to freeze several things, including Heimdall and the Rainbow Bridge device.
The Tesseract is a device that emits vast amounts of energy, and can be used to travel between the realms. This device was central to the plot of Avengers, and Captain America. It was not seen in Thor, except during the post-credits scene.
