What we believe is expressed through our actions, which is why James 2:17-18 says that faith without works is dead and that he would show his faith by his actions. Obedience to any set of instructions that are for our own good is about putting our faith in the one who gave them to rightly guide us, so if we have faith in God to guide us in how to rightly live and faith that His law was given for our own good in order to bless us (Deuteronomy 6:24, 10:12-13), then we will obey His law. In Matthew 23:23, Jesus said that faith is one of the weightier matters of the law, so only those who have faith in God will obey His law and be justified by that same faith, which is why Paul said in Romans 2:13 that only doers of the law will be justified, but did not say that we ear our justification by obeying the law. Every example of saving faith listed in Hebrews 11 are instances of people taking actions in accordance with God's will, while disobedience to God's law is referred to as breaking faith, such as in Numbers 5:6.
In Titus 2:11-14, our salvation is described as being trained by grace to do what is godly, righteous, and good, and to renounce doing what is ungodly, which is what God's law was given to instruct us how to do. Furthermore, verse 14 says that Jesus gave himself to redeem us from all lawlessness and to purify for himself a people for his own possession who are zealous for doing good works, so if we trust in the cross, then we will become zealous for doing good works in obedience to God's law (Acts 21:20) and will not return to the lawlessness that Jesus gave himself to redeem us from. At no point is trusting in the cross ever presented as something that we just mentally affirm to be historically accurate. Even the demons believe that Jesus rose from the dead, so we need to understand and trust in what the cross means for how we should live our lives.
Everything that Jesus taught in the Sermon on the Mount was in accordance with the OT. Kind of like a parent watching their toddler who is stumbling in the process of learning to walk, God wants us to succeed, He is cheering us on, and He has infinite patience for those who are seeking by faith to learn how to follow Him.