If you believe that God in the Old Testament is the God of the New Testament then you can be able to understand that they are one and the same God. There are many mysteries of the bible that many people do not know because they want to listen only to what they want to hear and do what they want to do. Even if they say they know God but they do not know His commandments and also His nature and characteristics.
They just say that they know that God is always good and that we can depend on Him always that He will guide us. If we could just have a faith in him then we could be saved. because of many people before who emphasized the law of the old testament that is why the apostles have emphasized that if we have faith in God we could be saved. If we receive Him then we can receive salvation. But faith is not enough if there is no action done.
That is why even if the apostles emphasized the faith they also followed the commandments of Jesus the savior who has come in the flesh. One example is apostle Paul who kept Sabbath day as a custom following Jesus who also kept the Sabbath regulation and law as was His custom so that people would follow His example. But the people rejected His commands and so we should not also do in this time so that we can be saved.