Possible to DIY moving a boulder?

We have a very large rock sticking out of the ground in the middle of our yard that really makes it hard to use the yard the way we want to (volleyball, soccer, etc). The rock is pretty huge – I dug around to find the edges and it's probably 6 feet long, obviously not 100% sure how deep.

Is it possible to move it using equipment rental from Home Depot or similar? Like there are 1.5-2 ton mini excavators available near me, but feels like that might not have enough weight to hold its ground moving something that large. There's also a 6' micro backhoe.

Alternatively, is it possible to somehow break the rock apart while it's still in the ground?