I'm not sure what you mean by "everything", but a substrate definitely can fit inside an enzyme!
Let's use the enzyme sucrase as an example. There's a vacant space in the enzyme called an "active site" where the substrate enters. In this case, sucrase's substrate is sucrose. The substrate "sucrose" enters and binds to the enzyme sucrase's active site. The binded sucrose and sucrase is called the "enzyme-substrate complex" because the enzyme and the substrate are present. This lowers the activation energy of a reaction, therefore speeding up the reaction as a result. The sucrose is converted into new products: glucose and fructose.
Enzymes are specific to their substrate because their active site only fits certain molecules. However, sometimes a similar-shaped item can fit in the active site and block it off :c