The term "early apples" usually refers to the first varieties of the season that get ripe. There are also mid-season and late varieties.
Around here, some early varieties are Yellow Transparent and Lodi. I've used them for cider, but it was kind of bland and I ended up blending it with cider from later varieties.
These days I only make cider from mid and late season apples.
Perhaps some folks call the unripe fruit "early apples", I've never heard that.
Most commercial orchards pick apples before they are fully ripened to avoid damage to the crop during handling and transport. From my experience, tree ripened fruit makes a better cider.
But experimenting with what you have is a good thing. You can let the unripe apples sit in onions bags in a cool place to allow them to ripen somewhat.
Keep checking them and if you start noticing any rot, go ahead and grind and press. If you have the freezer space, you can freeze the juice to add to later season cider or go ahead and ferment it and maybe use it to blend with other cider if it needs some help.