The way to believe in God is by directing our lives towards being in His likeness through being a doer of His character traits. For example, by being a doer of good works in obedience to God's law we are testifying about God's goodness, which is why our good works bring glory to Him (Matthew 5:16) and by testifying about God's goodness we are also expressing to belief that God is good, or in other words, we are believing in Him. Likewise, the way to believe that God is a doer of justice is by being a doer of justice in obedience to Him, the way to believe that God is holy is by being a doer of His instructions for how to be holy as He is holy, and so forth. This is exactly the same as the way to believe in the Son because the Son is the radiance of God's glory and the exact likeness of His character (Hebrews 1:3), which he expressed through his works by setting a sinless example for us to follow of how to walk in obedience to God's law.
This is why Bible frequently connects our faith with our obedience, such as in Matthew 23:23, Jesus said that faith is one of the weightier matters of the law. In James 2:18, he said that he would show his faith by his works. In Revelation 14:12, those who kept faith in Jesus are the same as those who kept God's commandments. In Romans 1:5, we have received grade in order to bring about the obedience of faith. In Romans 3:31, our faith upholds God's law. In John 3:36, it equates believing in Jesus with obeying him. In Psalms 119:30, he chose the way of faith by setting God's law before him. In Hebrews 11, every example of faith is of someone doing works. In Numbers 5:6, disobedience is referred to as breaking faith. In Hebrews 3:18-19, it equates disobedience with unbelief. And so forth.
Likewise, the reason why there are many verses that say that the way to have eternal life is by believing in Jesus and many verses that say that the way to have eternal life is by obeying God's law is because God's law is His instructions for how to believe in Jesus, or in other words, embodying God's word is the way to believe in God's word made flesh.