Here's how far I got. I wasted a lot of time at the beginning exploring my island from bottom to top then back to bottom before building my capital.
That's likely why you ended up so far behind, and running to catch up -- well, that and the fact that you're still running a Monarchic gov in the Modern era...
In both my attempts so far, I moved my Settler onto the NE Hill, and planted Delhi on Turn 2 (where you built Madras)...
I also built several size 2 hill towns that just produce military the whole game and only have a barracks.
I probably should have done that too, but I was more concerned with getting my best-sited cities up to maxPop ASAP, so I was building Workers for roading, Jungle-chops and mining, rather than spending pop-points on Settlers that would make only marginally-useful towns. As well as the standard Courthouses to maximise income and Ducts to get to Pop7+, since all my towns were/are coastal and low on SPT (obviously, I haven't got rails/ electricity yet), I've also cash-rushed a lot of improvements that I wouldn't normally, e.g. Temples for Cultural expansion over the Sea-tiles, Harbours to work those Culturally-grabbed tiles, and Markets to maximise commerce from them (not necessarily in that order, depending on location).
When I got War Elephants I invaded the Aztecs and got some good land but the Persians were too powerful.
Funny how things can work out completely differently in different people's games, huh? My first Wellies were rather used to take the AIs' beachead-towns on my lands, and trigger my GA. I am certainly eyeing the Aztecs as my next target, though: partly because they're closest, partly because they don't have Saltpetre, nor Rifles (yet), and partly because, well, it's Monty, and he always deserves it
Conversely, the Persians are (so far) nowhere near attaining superpower-status in my game -- I believe that honour currently belongs to the Mayans or the Hittites (one of whom, as I say, just went Industrial). I did actually manage to get a mainland town (with Dyes) off the Hittites shortly after my GA (roughly where Malinalcove is in your screenshot), which I intended for later use as a beachhead vs the Aztecs (it also would have been/will be again a useful town in its own right, having approx. 2nd-ring status from Delhi), but I was slack about reinforcing it, and lost it to a massive American Cav-assault a couple of turns later, while my v+eWellies were still healing -- while covered (I thought) by a rMusket. (Naturally, this assault happened on the same IBT after I'd just cash-rushed a Temple there... That same co-incidence strangely
also occurred in one of the AI-towns I'd acquired on my homeland...
)