So when the temple was destroyed in the 1st century, did it make following the law impossible? How many of the 600 + laws involve the Temple in Jerusalem? When was the last time the chief priest in Israel offered a sin offering for the nation in the holy of holies of the Temple?
Righteousness comes from faith alone. Works can confirm faith is genuine, but works do not provide righteousness... faith alone does that. This is why Abraham was made righteous for his faith DECADES before he offered Isaac on the altar. David speaks of the righteousness which comes without the law:
[Psa 32:1-11 NASB] 1 [A Psalm] of David. A Maskil. How blessed is he whose transgression is forgiven, Whose sin is covered! 2 How blessed is the man to whom the LORD does not impute iniquity, And in whose spirit there is no deceit! 3 When I kept silent [about my sin,] my body wasted away Through my groaning all day long. 4 For day and night Your hand was heavy upon me; My vitality was drained away [as] with the fever heat of summer. Selah. 5 I acknowledged my sin to You, And my iniquity I did not hide; I said, "I will confess my transgressions to the LORD"; And You forgave the guilt of my sin. Selah. 6 Therefore, let everyone who is godly pray to You in a time when You may be found; Surely in a flood of great waters they will not reach him. 7 You are my hiding place; You preserve me from trouble; You surround me with songs of deliverance. Selah. 8 I will instruct you and teach you in the way which you should go; I will counsel you with My eye upon you. 9 Do not be as the horse or as the mule which have no understanding, Whose trappings include bit and bridle to hold them in check, [Otherwise] they will not come near to you. 10 Many are the sorrows of the wicked, But he who trusts in the LORD, lovingkindness shall surround him. 11 Be glad in the LORD and rejoice, you righteous ones; And shout for joy, all you who are upright in heart.
[Psa 13:5 NASB] 5 But I have trusted in Your lovingkindness; My heart shall rejoice in Your salvation.
[Psa 78:22 NASB] 22 Because they did not believe in God And did not trust in His salvation.
Trust is the literal translation for faith in Hebrew. Habakuk also speaks to the righteousness of faith:
[Hab 2:4 NASB] 4 "Behold, as for the proud one, His soul is not right within him; But the righteous will live by his faith.