I am reading Higher Topos Theory to learn the properties of $\infty$-categories. I found that Proposition A.2.6.15 is used in Proposition 2.1.4.7 to give a construction of the covariant model structure. But Proposition A.2.6.15 uses some features that had not been introduced until Chapter 5, making its proof inaccessible before reading Chapter 5.

Is there any proof that avoids using those structures that are introduced later in this book?