This is a wall painting from Pompeii (my own photo).
Look at the roofs, the representation of the tree, and the color scheme. Remind you of any art style you’ve seen? And there are a ton of rooms in Pompeii decorated in red, black and dark green. It looks very much to me like someone in Pompeii had at least seen Oriental styles.
As for bypassing Persia, the Romans had trading posts in India. The sea route is obvious.