Of course you can. You started by saying the prayers of an unbeliever have no access to Him, then essentially told him to pray for faith. Pray to who if He is not listening to unbelievers?
(FWIW, I struggle with this very paradox in praying for the safety of Trump, I do it anyway.)
An unbeliever praying to God in intercession is totally unbiblical. Because there is no covenant relationship. The unbeliever is not part of the family, has no inheritance, nor any portion of the Kingdom.
That all changes when an unbeliever admits his helplessness and prays to God for salvation which is only possible through Jesus Christ.
That is Christianity 101. It is fundamental.