Persona 5 uses a variety of social stats that allow you to interact with different systems in the world as well as increase your relationships with others. Trying to get your guts up can take some time and come from a variety of sources. Guts will help you stand up to people in conversations, as well as increase your relationships with certain confidants.
In Persona 5, guts will be bestowed upon you frequently for seemingly random reasons. Often, guts are an additional bonus to something that you are doing. For example, if you choose to study in the school library, you will not only increase your knowledge, but also your guts.
If you want to raise your guts quickly, go and participate in Tae Takemi’s strange clinical trials. You will meet her fairly early on before Kamoshida Castle Palace. Let her test her strange concoctions on you for the good of your stats.
At night, you can also visit the burger place on Central Street. For a small price, you can attempt their Big Bang Burger Challenge. This is essentially a stat check, and if your character passes, you will be rewarded with a prize and a bunch of guts.
Going to the coffee shop and ordering coffee will also raise your guts as well as your knowledge. Similarly, working in the Crossroads bar will increase your guts periodically as well.
You can also read books to increase social stats. You can check out books from the school library, or you can buy them at the bookstore. On the description for each book, it will let you know which stat will be increased by finishing it. You can read books in the school library or occasionally on the train.