Constructed Decks
In the Ranked Constructed deck selection screen, MTG Arena only displays your legal decks (containing at least 60 cards and up to a 15-card sideboard, all from the current rotation, and generally no more than 4 of any card other than basic lands).
That said, if you can't find your deck, click on the Decks tab in case the cards in your deck are not yet legal for the Constructed format.
Preconstructed Decks
If you are looking for the preconstructed decks that are earned as part of the new player experience, those are unlocked by gaining XP (via completing quests, winning matches, etc.) after the tutorial.
For further troubleshooting, please visit our feedback page here to view a list of the latest known Magic: The Gathering Arena issues/bugs or report a new one.