Yeah, you've pretty clearly underinvested in military -- 1 composite bow (easily upgraded to x-bow) is not going to hold off multiple Carthaginian riflemen, cannons, etc. But the root cause seems to be undersized cities, and corresponding poor science rate.
Looks like you've left your cities on production focus for way too long. At this point, with full Tradition, your capital should be at or near 30 pop, but it's only at 18, and your other long-founded cities are undersized. And most are set on production focus, so your science specialists aren't being worked. Your overall beaker rate is 399 with 4 policies in Rationalism (through Free Thought). Just assigning your science specialists in all cities. and your 4 guild specialists (you weren't working guild slots either, so your culture rate is poor), boosted your beaker rate by 22% to 490. Still not great, but far better. I see you built the Great Library -- although you can get it on Immortal (as you did), the sacrifices are often too great -- working production tiles to bang out GL means little to no growth for too many turns in the early game.
Looks like you've left your cities on production focus for way too long. At this point, with full Tradition, your capital should be at or near 30 pop, but it's only at 18, and your other long-founded cities are undersized. And most are set on production focus, so your science specialists aren't being worked. Your overall beaker rate is 399 with 4 policies in Rationalism (through Free Thought). Just assigning your science specialists in all cities. and your 4 guild specialists (you weren't working guild slots either, so your culture rate is poor), boosted your beaker rate by 22% to 490. Still not great, but far better. I see you built the Great Library -- although you can get it on Immortal (as you did), the sacrifices are often too great -- working production tiles to bang out GL means little to no growth for too many turns in the early game.