Couldn't elephant have the same momentum as a golf ball

Yes, of course.

Momentum = (mass) x (speed)

If mass is very small, then a high speed can make up for it.

If speed is very low, then a large mass can make up for it.

If the elephant is lying there asleep, then he has no momentum at all ...

it's easy for any object to equal that, wouldn't ya say!

Yes but it's not very likely a elephant would most likely have more momentom