Slitherine

The default infantry is only strength 2 and the mercenaries are only strength 3, it seems only provincial units and the chariots are better. Is there any way to get better infantry than the Egyptian spear-carriers?

The Spearmen are actually 3-2, not 2-2 ... So use them in attack, if feasible.

Aside that, at CL 3, the Mercenary Infantry switch from Semitic to Hellenistic, so you can hire Hoplites (4-3). Aside that, you need provincial units or chariots to compensate.