Mayan vs Goths

Is this a total civ loss?

I played a 2v2 match, where it was basically just 2 1v1's, and I was faced against the goth player as the mayans.

I did a pretty decent fuedal archers push. Got a vill, made one weak, got a defensive tower, and I managed to park 6 archers on his main gold leaving his base open and off his main gold which he had a mining camp on.

To this point I feel good. I'm walled and focusing on fast castling. Beat him to castle. Drop 2 tc's and about 4 barracks. Pump out fully upgraded longswordsmen.

First to imp. Make a few trebs and continue pushing and making fully upgrade 2 handed swordsmen now. Take a few barracks and a castle before he just starts melting my infantry.

Tried teching into fully upgraded eagles but they also got wiped but maybe the numbers where too disproportionate at that time?

Is this matchup just a total civ loss once it gets late? Is there a plausible army compensation against goth spam?

Should i just commit to a 1tc early castle push instead next time rather than the eco approach?