When you use the phrase "the silence of God", there's really two levels when we might think about that. There's the big, broad level. Biblically speaking, God at times is silent.
The period between the Old Testament and the New Testament is frequently nicknamed the silent years, the 400 silent years in fact. The book of Amos says that when God does not speak, that is the judgment of God. And then of course though, after those 400 years of silence, the book of Hebrews tells us that having heard from the prophets, heard from God through the prophets in the past, now in the person of Jesus Christ, the revelation of God has exploded forward.
But that's maybe not the question you might have. Your question might be, why does God seem silent in my life? Why am I not hearing from him? Why do I not see him working? Well, the good news is for you is that in that sense, God is never silent.
He is always working behind the scenes. He is always providentially and sovereignly carrying out His will, even when it seems like nothing is happening. So you can take great hope in that truth.