In gentleness of spirit, upon encountering an atheist quickly pray within yourself to God and tell God you forgive the atheist for all their sins and ask God to also forgive them… this allows God to forgive them without them repenting… once their sin is removed there is no barrier between them and God… temporarily.
Now, speak to them… just ask the atheist if they could know the truth if God does or doesn’t exist, would you want to know the Truth?
If they confess they want to know the truth, then they have given Jesus Christ an open door…
Next. ask what led them to their decision to not believe that God exists…. this will take a while… you’ll have to go back with them through their decision process to uncover the lies… give them Truth… with God’s Love and gentleness.
if you encounter pride, there’s nothing you can do for them. It will take humility to want to know the Truth.
Keep them in your prayer list and perhaps there will be another opportunity to help them.
No arguing, no strife… just God’s gentleness and wisdom.