Saying that The Legend Oof Zelda: Tears of the Kingdom is a big game is like saying the sun is hot. It goes without saying, but you'll only really understand the true depths of that statement after you've stared at it for long enough. Then the world opens up completely. From here you can blast your way to any of the game challenges.
The tutorial has a soft ending when you leave the Garden of Time, but for the sake of world exploration, the tutorial doesn't truly end until you get the glider from Purah. From there, the critical path is entirely determined by you, which can paradoxically make decisions really hard to decide on. These goals can help focus those early hours of confused wonder.
7 Champion's Leathers
After Link is shot into the sky by a sky island, he mysteriously finds himself naked in a cave for the second time in his life. His shirt has been whisked away by Zelda somehow, as loosely confirmed by a diary entry in Hateno, and now it's hidden away in Hyrule Castle, meaning you can get this armor on your first visit to the floating section.
To unlock the Champion's Leathers you will have to light several torches in the throne room above where you fought Ganon in Breath of the Wild. Light all the torches in the room and a secret entrance will be unlocked. The armor boasts a respectable defense stat, and it will also allow you to shoot beams with the Master Sword at any health level.
6 Hylian Shield
The Hylian shield is also found in Hyrule Castle, and it can be found without flying to the floating area. Instead, you will find the shield hidden away on the back side of the moat, in the dock area. In the far back, there will be a platform with a single brazer that can be lit. Once done, the Hylian shield will be yours.
This is easily the strongest shield in the game. The defense stat on shields isn't explained in game, but what it actually tells you that it will disarm enemies you parry when they attack with an attack rating lower than the defense rating, and if enemies will stagger when attacking your blocked shield. Finally, it also reads how much durability will be lost when struck, meaning this shield will rarely take more than one point of durability damage. This might make you hesitant to use the shield, because it's so precious, but you can always buy a replacement from Cece.
5 Soldier's Set
The final piece of treasure that can be found near Hyrule Castle, and which will truly change your early game, is the Soldier's Set found in the Royal Hidden Passage Cave. This is a decently long mini dungeon, with a proper boss at the end. Every armor piece, however, is hidden in seemingly benign rooms, making this incredibly easy to miss.
The Soldiers set doesn't have a special ability, but it does have the highest defense stat in the game, at a staggering 84 when fully upgraded. This more than makes up for the lack of a bonus ability. It will save your life more than once until you can unlock more heart containers, and you can start to slowly retire this set for the bonus of another.
4 Activate Every Tower
Having a blank map in Tears of the Kingdom doesn't feel great. It just feels bad on the eyes, and on the adventure seeking soul. How can you adventure properly when you don't even have reference for where you are? This is why you can, and should, unlock every tower as soon as possible.
Not only will the towers allow you to actually see, but they will also be your springboards into the world. So, the more towers you have, the easier you can explore. The easier you can explore, the more loot you can get. It's a simple exchange, but an effective one that will cost you sleep.
3 Glide Set
If you have all the survey towers, you will be able to get the Glide Suit rather easily. There are three dive challenges spread between the skies near Lindor's Brow Tower, Typhlo Ruins Tower, and the Mount Lanayru Tower. You will have to pass a time trial given by a Construct, and he will give you one of the three pieces.
Being able to access these sky islands so early is a blessing, because you will spend a lot of time gliding and soaring in this game. To top it off with a bow, the upgraded Glide Suit completely negates fall damage. You can teleport midair, so dying from a great high probably isn't that common, but it's still fun to crash Link nose first into the ground at mach three.
2 Hyrule Gazette
As you begin to move from the early game into the main story, you will want to make sure you picked up the Hyrule Gazette quest chain in Hebra, near Rito Village. This quest chain will take you to every stable on the map, and it's better to just get them done as soon as you get to a new stable.
Additionally, the chain offers a pretty serious reward. For different milestones, you will be rewarded with the Froggy Suit, which will make you nearly slip proof. That is unless you upgrade the suit to level two, and then you will be fully slip proof. This revolutionizes the game. Some puzzle rooms are quite literally designed to be easy if you could climb, but it's either raining, or the walls are made of ice. This suit just ignores that.
1 Start The Kohga Quest Chain
The Depths/Kohga quest chain is another important one that you should start as early as possible, and the first fight can be done as soon as you can reach the underground. The first battle takes place in the Central Mining Facility directly under the Goddess Statue on the Great Plateau. A sinkhole in the Eastern Abbey nearby will drop you next to a minecart rail that will take you the rest of the way to the facility.
The reason this should be tackled so early is because of the ability it gives you. This first mining facility will unlock the Autobuild feature, which will save you actual minutes, if not hours, building the same contraptions. You will unlock schematics, as well as be able to set favorites, but you will also have a history where you can select from recent builds. It's the best quality-of-life feature in the game, and you need it.