My most successful games as Japan have been less about conquering neighbors and more about just fighting them and killing their units to farm unit XP in order to get Great Generals and bonus promotion yields. Authority or Tradition can work equally well for Japan depending on who your neighbors are. If you have warmonger neighbors then you'll have an easier time going with Authority, and if you have peacemongering neighbors you can get away with Tradition. The point is that although Japan's UU and UB are good for warfare (Samurai are one of the best combat units in the Medieval/Renaissance Eras save for Impi and Caroleans), their UA is wonderful for Great Person generation and achieving a Cultural Victory.
You already understand the synergy between God of Protection and Japan's UA, but you will need a medium-sized empire as quickly as possible in order to generate enough faith to guarantee founding a religion. I usually go with Animal Husbandry or Mining as my first tech, followed by Pottery, and then B-line for Military Theory or Construction depending on how many horse/quarry resources I have access to. I try to settle at least 4 cities around my capital as soon as I can (although I try to time the settling of my 3rd+ city for after I get Imperium if I go Authority for the extra yields), and then if there is extra space I will settle more. But the important thing is getting Barracks and/or Walls up in my new cities as soon as I can. The extra production per city from Authority REALLY helps here, and is one other reason I prefer it over Tradition, even if I want to go for a Cultural Victory. So once Military Theory and Construction are unlocked my new city build order becomes Barracks > Walls > Shrine/Monument > Council. Sometimes I will delay building Shrine/Council to build a military unit, especially if I have warmonger neighbors.
In order for this to work though you need good efficiency and a source of gold income. All of those Barracks and Walls and military units are going to put you into negative Gold per turn quickly, so you need a way to generate income to pay for it all. If you have gold-rich luxury resources around (Gold/Silver/Gems/etc) then that really helps, but if you have food/culture focused luxuries then you will likely need to trade with your neighbors or war with them to generate gold so you don't go broke before you can research Trade and build Markets. If there are some City States nearby you can also try bullying them for gold. If I don't have good luxuries to work/trade I will often declare war on a neighbor and pillage their improved tiles for gold, and then try to get a good peace deal with more GPT from them in order to supplement my income even more. The point is, if you focus entirely on building military buildings for the bonus faith/culture and you don't watch out, you'll go broke and be in big trouble!
If you can found a religion then you should be set for whatever you want to do next. You can use your religion to enhance your fighting ability or reinforce any other areas you may be lacking on. Just about any of the Founder beliefs can be useful depending on if you want to win via Domination or Culture. Holy Law, Ceremonial Burial, and Hero Worship are my top picks but Council of Elders is also great. If you're doing poor on Gold then you can always take Thrift as a Follower belief, and Orders are a great choice for a faith building if you don't want to further focus on food/production/science/gold yields.
Once you unlock Steel then the real time for warfare has come, although you might have to take a few cities once you unlock Bronze Working if you don't have enough Iron within your borders. If you want to win through Domination then it's time to get to work crushing your neighbors, but if you want to do a Cultural victory then all you need to do is kill units. "Farm" your neighbors by declaring war, pillaging their improved tiles for gold, and killing most of their units to gain science/culture yields and XP for promotions and Great Generals. You can use this to get a leg up into the Renaissance/Industrial Eras where your land units are no longer as useful and then worry less about fighting and more about working Guild specialists, generating Wonders, and reaching Archaeology. Personally, I find it much easier to win Culturally with Japan than through Domination, especially on higher difficulties, but you do whatever you're more comfortable with. It's also entirely possible to swing either of these victory conditions into the other in the late game if you find the path you wanted to take too difficult. Winning wars and generating Great Generals/Admirals will net you lots of tourism!
