Building research is definitely not the best way.
Your problem seems to be city placement. 5 cottages for 6 cities is a little bit too few, it seems like. I replayed your initial save from the beginning till 800AD.
I build 4 cities and got Iron Working and Monarchy early. While the nearest copper mines are in horsehockey places, the iron mine is in a good one, although far enough. The good news is that you don't need Iron for Jags, so with Jags and Chariots you have decent defenses.
I also moved the capital, it took a while, but now it's in a high-cottaged city, and with some production, too. I set up for researching Civil Service.
I skipped Alphabet since with that capital placement there seems to be no way you can compete with the AIs. However you still have some room for peaceful expansion, there is a good city spot near the Corn resource on the East. Also, I fortified a few units near the barb city on the West, waiting until it's size 2.
Once the cottages mature, the UBs are built, and some GS are generated for the Academies, things will be better. I expect to start tech trading after CS, it's very likely some of the AIs won't have it by that time.
Then get Construction and start building army.
