We use our Assembly Time mostly for Music. Our Sunday school is before worship so we preview some worship music and reinforce Rotation learning with our unit's music. This works well because, no matter when you arrive, you can participate fully.
An article I ran across just today for children older than pre-school is based on Legos. You can find it at Building Faith Brick by Brick: Formation with Lego by Emily Given.
(Talks about how boys love Legos, but my 4 granddaughters adore Legos, too.) It's from an Episcopal publisher, but looks very usable by other denominations. The "early arrivals" might even put together some Legos that would help tell the morning's story.