The Bible is very clear and you are concentrating on a couple verses taken out of context.
Did God’s plan of salvation change?
Were some men justified by works, ever?
You claim that an act must be performed by men for salvation, meaning that a person can repent, believe, and have months go by before baptism and only then are they saved.
Did the thief on the cross get baptised?
God’s plan is the same for everyone, always was. Always will be.
Salvation by faith, through grace.
Nothing else.
Rom 4:1 What shall we say then that Abraham our father, as pertaining to the flesh, hath found?
Rom 4:2 For if Abraham were justified by works, he hath [whereof] to glory; but not before God.
Rom 4:3 For what saith the scripture? Abraham believed God, and it was counted unto him for righteousness.
Rom 4:4 Now to him that worketh is the reward not reckoned of grace, but of debt.
Rom 4:5 But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness.
I’m so glad I was made aware of my sins, by faith came to God for the remission of my sins by appealing to Him in the name of His dear Son and his substitutional death on the cross where he bore my own sins in His body on the tree, and received forgiveness of sins by faith in His finished work, and then, rose and, in obedience to His command, was baptized, acknowledging to the world around me that I have been crucified with Christ, nevertheless I live, yet not I but Christ liveth in me and the life which I now live in the flesh I live by the faith of the Son of God who loved me and gave Himself for me.
James 2:17 Even so faith, if it has no works, is dead, being by itself.
James 2:18 But someone may well say, "You have faith, and I have works; show me your faith without the works, and I will show you my faith by my works."
James 2:19 You believe that God is one. You do well; the demons also believe, and shudder.
James 2:20 But are you willing to recognize, you foolish fellow, that faith without works is useless?
James 2:21 Was not Abraham our father justified by works, when he offered up Isaac his son on the altar?
James 2:22 You see that faith was working with his works, and as a result of the works, faith was perfected;
Even Abraham had to obey God to be justified by (obedient) faith. There IS both (obedient) faith and works involved in salvation. Man must obey God and THEN the grace through Jesus kicks in. The Bible is clear.