One way atheists sometimes argue against God is to highlight one area of life in which, in their mind, the Christian actually doesn't trust God. Why keep a fire extinguisher if you trust God to stop your house burning down? Why go to a doctor if you trust God to heal you? Why carry a weapon if you trust God to protect you? These things, and more, are all things atheists think prove Christians don't really trust God. In reality, all it proves is these atheists have no idea who God is.
The Bible is filled with far more than just "trust God, He won't let anything happen to you". In fact, "He won't let anything happen to you" is not in there at all. Quite the opposite, the Bible tells us that in this life, we will face trials and tribulation, and that these things develop our character and cause us to trust in God more. The Bible also contains wisdom. Wisdom is all about general principles which, if applied, have a high chance (but do not provide a guarantee) of the best outcome in life. Wisdom includes preparation, adequate management of resources, correct responses to given situations, and a range of other things that uneducated unbelievers might perceive as a lack of trust in God.
In other words, if I trust God, it actually makes sense to prepare for the troubles a human being can face in this world. After all, we're still in it! If I really trust God, I must trust not that He will protect me from the consequences of my own foolishness, but that by avoiding foolishness, I have a greater chance of living a full and fruitful life. Saying "if you trust God, you wouldn't do this wise thing" is like saying "if you trust your seatbelt, you wouldn't wear it". I wear my seatbelt because I trust it. In the same way, I act wisely, as the word of God says I should, because I trust God.
God never promises we'll escape any bad situation just by trusting Him, but there is a promise He does make. When you put your faith in the death and resurrection of Jesus Christ, you will inherit eternal life in a Kingdom where God does ensure prosperity. Alternatively, you can die in your sins and be condemned. In Hell, there are no fire extinguishers, and no doctor can heal the wounds received there. Come to the eternal doctor, Jesus Christ, before your sin kills you.