A couple of months ago, start of winter here, I bought a "bonsai starter"
Olive tree. It's only about 2-3 inches tall,
Now it's almost the end of winter, and I have noticed that the leaves are
starting to get larger, some of them have doubled in size.

It is axiomatic in bonsai that the LAST thing you worry about, when the trunk
and branches are completed & it is ready for show, is the leaf size. I assume
you mean Olea europaea, but it is true for any species.
Right now it is a baby, and should be allowed to grow freely. The leaves may be
larger simply because of its growth stage, or because it is in less light than
it was at the nursery.
In general, the contributing factors to small leaf size a
Avoid excessive fertilizer. (After the tree is full grown.)
As much light as possible. For an olive, full sun.
Brisk air movement.
Repeated pinching of growing tips.
Don't ignore the factor of starting with a small leaved variety. In this
country we have an excellent dwarf cultivar 'Montra,' usually sold as "Little
Ollie." It is widely used in California as a backyard tree, and has become the
standard for olive bonsai where you can't get collected ones.
Iris,
Central NY, Zone 5a, Sunset Zone 40
"If we see light at the end of the tunnel, It's the light of the oncoming
train."
Robert Lowell (1917-1977)