It seems to me that God is not the kind of being that seeks for you to be lazy. We shouldn't just wait and "trust in God" to help, solve problems, or make good things happen.
That kind of laziness does not seem to be consistent with the teachings in the Bible or other sources. Ignoring your own ability to think, decide, and take action is the easy way out.
Often this is expressed as, "I don't need to do something because God will take care of me." Or, rather than learning, understanding, and making a decision, the sentiment that, "I just trust in God." Lazy thinking and lazy in the lack of action.
And, it seems to me that God gave a powerful brain to each of us for a reason. We are to use it. Go forth and strive to understand the world. Gain insights, and from those, develop solutions to challenges and problems that enhance life for us all.
Not using the resources provided—like our powerful mind—is disdainful of God's gifts. We were provided with the unique ability to understand the world using tools such as the scientific method so that we can learn, improve and do more. In particular, we can and have made life better for all with improved sanitation, medicine, and public health. How disrespectful it must be to God when we ignore these mental and physical gifts by think poorly, or in the height of laziness no thinking at all, and just leave issues to God to solve.
How is this different than when your children claim they are not picking their stuff up and putting items away because you can do it better for them. Of course, your response is, "how are you going to learn unless you do it yourself." Do you think God needs your problems to solve too? Particularly without you even trying? Likely it's just as annoying to him as your children can be to you.
Although the Bible does not contain the quote "God helps those that help themselves", as many seem to believe (more on that below), there are some passages from the King James Bible that suggest that God takes pleasure on those that take ownership for themselves and their problems:
12:11: He that tilleth his land shall be satisfied with bread: but he that followeth vain persons is void of understanding.
12:24: The hand of the diligent shall bear rule: but the slothful shall be under tribute.
13:4: The soul of the sluggard desireth, and hath nothing: but the soul of the diligent shall be made fat.
28:8: The LORD shall command the blessing upon thee in thy storehouses, and in all that thou settest thine hand unto; and he shall bless thee in the land which the LORD thy God giveth thee.
5:8: But if any provide not for his own, and specially for those of his own house, he hath denied the faith, and is worse than an infidel.
Further, in Islamic texts:
Trust in God But Tie Your Camel is an Arab proverb. It is one of the reported sayings of the Islamic prophet Muhammad. Don't just trust in God and expect all the work to be done for you. Do what you can.
According to Tirmidhi, one day Mohammed noticed a Bedouin leaving his camel without tying it.
He asked the Bedouin, "Why don't you tie down your camel?" The Bedouin answered, "I placed my trust in Allah." At that, Mohammed said, "Tie your camel and place your trust in Allah."
George Herbert included "Help thyself, and God will help thee" in his proverb collection, Jacula Prudentum in 1651. But it was the English political theorist Algernon Sidney who originated the now familiar wording, "God helps those who help themselves", apparently the first exact rendering of the phrase. This is the first use of the familiar modern English phrase that best captures this concept. Benjamin Franklin later used it in his 1736 Poor Richard's Almanack, which has been widely quoted.
In my view, we should use every skill and bit of knowledge available to us to do for ourselves as much as possible and as best possible. Do everything you can do. Use the available facts to feed rational thought. Exercise your mind. Be a life long learner. Trust that God will respect your efforts, look favorably on your use of the tools that were made available for us all, and reward it. Doing anything less is an insult to what has been provided to us.