That looks like a pine tree seedling. If the needles are still soft, it has a chance at survival. There's nothing you can do, beyond normal care, to make it live.
Your tree has many years to go before it can be considered a bonsai. Bonsai is a pruning and training style and has nothing to do with pot size. Your tree will not be able to grow into a bonsai tree unless you find it a much bigger pot (but don't do any repotting until its healthy).
Those tiny pots are the end of the process, many many years down the line.