In Νόμων Ἱερῶν Ἀλληγορίαι, (Legum Allegoriæ), Stoic Philosopher Philo of Alexandria sets out to make an allegorical commentary on Genesis 2-3. Why does Philo choose to pick up with chapter 2 instead of also addressing Chapter 1 of the creation story of Genesis?
Genesis, in fact, contains (at least) two creation stories. The first ranges over Gen 1:1–2:4a; the second over Gen 2:4bff. The exact boundaries are debated. See e.g. Zevit, 2013, What Really Happened in the Garden of Eden?, esp. pp. 76–77:
Originally, the Hebrew Bible did not have chapter divisions. It was written as a continuous text with breaks approximating paragraph divisions where narrative scenes or topics under discussion changed. Chapter divisions and verse numbers were first inserted into biblical texts during the Middle Ages by Christian scholars as a way of dividing the text for ease of reference. (...)
One consequence of this medieval misdivision has been uncertainty as to where the seven-day creation story ends and the Garden story begins. Although many scholars consider Genesis 2:3 to be the end of the Cosmic Creation story, others propose that it ends with the summarizing statement of Genesis 2:4a. If so, then the Garden story proper begins only at Genesis 2:4b.
Arguments in support of the second position follow a twofold line of reasoning. On the one hand, verse 4a seems an appropriate summary of the creation narrative; on the other, if verse 4a were the first line of the Garden story, verse 4b would be unnecessary because it repeats the same information.
So, Philo doesn't really skip part of the story, he just considers a different story. In Legum Allegoriae, Philo writes how "the history of primal man is (...) considered as a symbol of the religious and moral development of the human soul." For this, the Garden story is much more relevant than the cosmological account of creation. However, not having access to the current knowledge that the Eden story only starts around 2:4, he also deals with vv. 1-3. This is described in the analytical introduction to book I (pp. 140–145 of your PDF):
In 1-18 Philo deals with Gen. ii. 1-3, which tells first of the completion of Heaven and Earth.
Philo does consider Genesis 1 in De Opificio Mundi. As a book of laws, that is "fitly prefaced by a Cosmogony" (analytical introduction to On the Creation, p. 2):
26 Then [Moses] says that "in the beginning God made the heaven and the earth," taking "beginning" not, as some think, in a chronological sense, for time there was not before there was a world. (Gen 1:1)
29 First, then, the Maker made an incorporeal heaven, and an invisible earth, and the essential form of air and void. (Gen 1:1)
30 Special distinction is accorded by Moses to life-breath and to light. The one he entitles the "breath" of God, because breath is most life-giving, and of life God is the author, while of light he says that it is beautiful pre-eminently: (Gen 1:2,3)
69 After all the rest, as I have said, Moses tells us that man was created after the image of God and after His likeness (Gen 1:26)
Also helpful is the analytical introduction to De Opificio Mundi on pp. 2–5 and the list of biblical references on pp. xxviii ff. of the PDF you linked (Op for De Opificio Mundi; L.A. for Legum Allegoriae).