To begin, when we talk about God in regards to His perfection – we can speak of His perfection in two ways – which then lead to the necessary conclusion that He is infinite.
God is therefore necessarily the explanation for His own reason for being. All other things – the universe, people, planets, angels and so on do not possess this quality of aseity or essential completeness. God would be God with or without the created order – and chose to create out of sheer pleasure and desire to overflow His unending glory (Habakkuk 2:14; Romans 8:22-25). Hence God is essentially perfect (Psalm 89:14; James 1:17).
The second way God is perfect is in regards to His moral perfection. God is fundamentally good through and through. Whenever Moses requested God to reveal His glory – God, Yahweh, responded by putting on display His “Goodness” (Exodus 33:17-18). All other moral perfections with holiness leading the list (Isaiah 6:3) include God’s mercy, grace, justice, wrath, benevolence and love for His people (Exodus 34:6; Jeremiah 10:23-24; Habakkuk 1:13; Jude 1:24-25). Such a being as God must by necessity be infinite and hence infinitely perfect. God’s moral perfection asserts He is the Absolute standard by which all morality is measured. Hence, “goodness” and “badness” do not become such when God declares them to be so. Rather, God being His own standard of goodness, holiness, love and so on is the final Determiner of what is good.
In order for God to function as essential and moral perfection – He must by necessity be infinite. By essence (i.e Being) He is unchanging or immutable (Malachi 3:6; Hebrews 13:8); not fully comprehended by any lesser mind (Romans 11:33-35); having no boundaries to mark His presence or immensity (1 Kings 8:27); without beginning nor end with regards to His duration (Psalm 90:1-2; Hebrews 1:5-14) and the Creator of all things (Genesis 1:1; 1 Corinthians 8:6). Moreover, Scripture reveals that such a God must then be all knowing or omniscient (Psalm 147:5; 1 John 3:20); all powerful or omnipotent (Psalm 139:13-16; Matthew 28:18); everywhere present or omnipresent (1 Kings 8; Psalm 139:7-12; Colossians 1:16-18); all wise (Psalm 139:22-24; Jude 1:24-25) and as already mentioned – all good (Psalm 139:17-22; Matthew 19:17).
Therefore in conclusion, we can note that: 1). God is both essentially and morally perfect. 2). God by necessity is infinite. 3). God is therefore infinitely perfect and by converse, perfectly infinite.