There is no direct attack damage stat in Breath of the Wild, however, it is possible to increase Links attack damage in a couple of different ways. This will definitely be much more valuable to you late on in the game as you are dealing with enemies that are much stronger than you are.
The first thing is, of course, the weapon you use. You will find more powerful weapons as you progress. Generally, the enemies that are strong will also drop strong weapons, so you shouldn't worry about this too much. If you progress slowly instead of rushing into the final stages, you won't be needing to use a rusty sword with 5 attack against a guardian.
Armor Can Increase Links Attack Damage
Yes, you read this correctly. The type of armor you are wearing can increase Links Attack Damage. Not all armor has an enchantment, but if you read over the armor & clothing section of the Breath of the Wild walkthrough on this site, you will see all of the different armor sets and the enchantments that they provide. One armor set in particular is the Barbarian Armor set. You will see that this armor set provides an all-round attack boost for each piece of the armor you obtain. If you have the complete set, you will see a nice increase to attack damage with all weapons.
Food and Elixirs
You will discover early on in the game that certain foods and elixirs can provide Link with some kind of enchantment, such as a resistance to the cold or the heat. Another such enchantment can come in the form of an increase to your attack. The cooking & recipes section to the BotW walkthrough also has a section on this. There is an elixir called the Mighty Elixir that will increase Links attack damage and there are 2 similar cooking recipes that increase attack damage.