It's hard to comment much without many screenshots, but I will say that I have long held that slingers are poor investments and almost always a mistake. The slinger itself is worthless in battle even vs. barbs, a lone slinger is not strong enough to reliably escort a settler vs. a barb warrior and therefore the slinger build risks delaying the settler. The upgrade cost for slinger > archer is not efficient, the archery boost is a just a few beakers of science ... and in my experience the slinger kill to actually achieve the boost is a tossup anyway, and even when a slinger kill is possible it often takes just as long or longer to set up the slinger kill as is it would have taken to ignore the boost and hard research Archery without the boost.
I also don't know how much warning you had for TheArchduke's military power spike, or what you were building at the the time that could have been switched to military. If your initial slingers had been warriors fortified in defensive positions, and then follow up with a 3rd warrior and a pair of archers that may have been enough to hold. Or at least divert the attack to a different opponent. Also the mere fact that Aztecs are your neighbor could have prompted you to bump your own military power earlier. If you posture spiky from the start, that could discourage TheArchduke from even going down the rush route even beginning.
If you can post a screenshot of your science and civics trees with some comments on the sequence and approximate time that you researched them I might be able give more pointers there. You have horses at the 2nd city site ... Were horsemen reachable? Maybe you could have saved gold for a horseman insta-buy on the turn you reach HBR. The mere fact that you could do this might sway TheArchduke against attacking. And the once you are certain that it is safe, the gold could actually be deployed for peaceful development purposes.
There are times to play for the long game, and there are times to get spikey in order to reach the long game. Again it's hard to talk specifics without screenshots, and I'm pretty rusty on my Civ6 mechanics. It's possible (or probable) that the combination of your start location combined with TheArchduke's Aztecs doomed you from any chance of ultimate victory from the start. And in that case a secondary goal of "Don't Die to the Aztecs" might be the real objective that is a "win" for this start. And choosing that win condition for yourself might change the weight of the decision that you make for your civ. Instead of a 150-200 turn ultimate victory timeline, maybe you are really playing to maximize your turn 80 potential, and then make your stretch goal "Survive to the End Game".
I also don't know how much warning you had for TheArchduke's military power spike, or what you were building at the the time that could have been switched to military. If your initial slingers had been warriors fortified in defensive positions, and then follow up with a 3rd warrior and a pair of archers that may have been enough to hold. Or at least divert the attack to a different opponent. Also the mere fact that Aztecs are your neighbor could have prompted you to bump your own military power earlier. If you posture spiky from the start, that could discourage TheArchduke from even going down the rush route even beginning.
If you can post a screenshot of your science and civics trees with some comments on the sequence and approximate time that you researched them I might be able give more pointers there. You have horses at the 2nd city site ... Were horsemen reachable? Maybe you could have saved gold for a horseman insta-buy on the turn you reach HBR. The mere fact that you could do this might sway TheArchduke against attacking. And the once you are certain that it is safe, the gold could actually be deployed for peaceful development purposes.
There are times to play for the long game, and there are times to get spikey in order to reach the long game. Again it's hard to talk specifics without screenshots, and I'm pretty rusty on my Civ6 mechanics. It's possible (or probable) that the combination of your start location combined with TheArchduke's Aztecs doomed you from any chance of ultimate victory from the start. And in that case a secondary goal of "Don't Die to the Aztecs" might be the real objective that is a "win" for this start. And choosing that win condition for yourself might change the weight of the decision that you make for your civ. Instead of a 150-200 turn ultimate victory timeline, maybe you are really playing to maximize your turn 80 potential, and then make your stretch goal "Survive to the End Game".

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