See the Trinity in this verse? We can come directly to the Father - no human intermediary needed. Even as a Pastor I need to help Christians understand that they have access to the Lord at His throne of grace just as any pastor or missionary might. Also, it is the Holy Spirit who aids us in our coming to the Father in prayer. He aids us in our praying but He also gives us the assurance that we are welcome in God's presence. And how is this possible? Because of what Christ has done for us - He cleansed and forgave us; He declared us righteous in His sight; and He brought us to His Father.
Let's not overlook the fact that Paul is speaking to both Jews and Gentiles. He emphasizes "all of us" can come to God. And we all come through the Holy Spirit. Read Acts 11:15 and notice how the Jews were surprised that the Holy Spirit came down on Gentiles just as He did on the Jews.
You can come to the Father because Jesus saved you and the Holy Spirit is always eager to bring you into God's presence!