20 turns is a long time. This is a really interesting question because a detailed answer needs some math. The 1 civic costs a lot because of how social policy costs scale. Policies 1 through 4 combined cost at least 565 culture, while the 5th policy costs at least 520. That is a lot of barbarian kills.OK, but if you have eg.: 100 per turn culture by that time its only 20 turns not counting barb kills. You maybe wont get that much if you stick to Auth, but picking another one immediately after Auth 1 could do the trick. I don't see how is +1 civic so taxing. At most it delays your progress by -1 civic at midgame or late game. But maybe having a -1 civic at late game a big deal since you delay ideology pick? Don't know. But in the early game even on Diety I can keep pace on civic count with others until sometime renaissance when they start running away. And if I don't pick it I'm already behind them in ancient era.
Here's an older thread about this (exact numbers may be off cause its old: https://forums.civfanatics.com/thre...la-for-determining-social-policy-cost.657988/ )
If your goal is to reach 5 total social policies as quickly as possible, then starting with authority 1 will be faster. However, if your goal is to reach a specific social policy, you'll find that starting with authority slows you down a lot. Reaching specific policies should be your goal, as the mid and late game social policies are really powerful compared to just 1 hammer per city in authority.
I've tried mixing tradition/progress with authority before, and it notably hurts your science. It takes longer to reach tradition's scientist or progress's 3 per city connection (even if you don't have city connections yet, 3 in the capital is a big boost).