Of course unsaved can do good works, but those aren't stored in heaven. Those works were self purposed. Look at me; I gave to charity.
As in my post,
Ephesians 2:10 - For we are His workmanship, created in Christ Jesus for good works, which God prepared beforehand that we should walk in them.
There is no way an unsaved person can do the works which God has prepared beforehand to walk in them, without being saved in Christ.
Those goods works of Eph 2:10 are required of the Christian, without those good works the Christian becomes fruitless and lost.
For we -- those who are Christians
are His workmanship -- one cannot make himself a Christian apart from God's instructions found in the NT. Therefore it takes obedience on the part of man to obey those instructions whereby one then is God's handiwork. It is those who are obeying God's instructions that "
work out your own salvation" therefore it is the obedient that God is working in, (Phil 2:12-13)
created in Christ Jesus -- this new creature (2 Cor 5:17) is created when men obey Christ (Gal 6:15 cf Gal 5:6; 1 Cor 7:19) obedience in submitting to baptism puts one into Christ (Gal 3:27).
for good works -- Christian are to serve by doing good works which salvation for the Christian is impossible apart from doing good works, the Christian must maintain good works (Titus 3:14; Titus 2:14; Heb 10:24; Matt 25:31ff)
which God afore prepared that we should walk in them -- 'afore prepared' means God has already indicated in His NT the good works Christians are to do showing how Christians are to walk in their daily lives (Rom 8:1,4; Rom 13:13; Eph 5:8; Col 1:9-10; Col 2:6; etc).
My point is that any man can do good works listed in the BIble (give to the poor, help the weak, feed the hungry, visit those in prison, do unto others, etc) but those good works
cannot save for it takes
obedience to God's will to be saved. And from the Jews in Acts 2 and Gentiles in Acts 10 we see that lost people can do the work of obeying God's will while still lost apart from God.
I do not know your theological background, but some theologies, as Calvinism, falsely teach man is born totally depraved therefore unable to do any good, man cannot obey God unless God first miraculously acts upon a person "regenerating" that person. So I am not sure what direction you are going when you said "
Without Jesus Christ in your life you can do nothing good." Are you suggesting by this statement that man is born totally depraved unable to do good works, unable to obey God unless first acted upon by God?