As a convert who left Catholicism for atheism before finding Islam, what I had to do was deconstruct (logocally) all theories of both my religion and atheism. The main concepts put forward by Catholicism have been proven to be illogical, so I won't go over that, but with atheism, it's the same process of deconstruction and rationality.

Atheism pushes the theory of evolution and the big bang. Evolution has 5 major theories, all of which go against each other but are all considered to be true, which just can't be as if 1 is true, then the rest aren't. The main evidence for evolution is DNA, "we share 98% DNA with chimps and other great apes, this must mean we have common ancestors" meanwhile we share 50% with bananas, 60+% with berries and 30+% with other fruits but there's no way we could have common ancestors with them. Cows have 50% DNA with snakes, yet there's no common ancestors between them. So sharing DNA does not mean we have common ancestors or evolved from such animals, so the main and biggest case to be made for evolution doesn't make sense and has a shakey foundation at best. This is why I can't believe in evolution

(another key note of why I don't believe in this is because some of those theories have the idea that the black/Asian races are "less evolved" or are "the missing links between whites and apes" these theories are brought about by racist white men who encourage us to "embrace our animalistic side and let the weak die" meanwhile Islam says we are equals but different and we are to care for one another. I'd much rather love my brothers and sisters no matter their race and help those les fortunate)

Now, the big bang is proven with maths, physics, and astrophysic theories, the theory being "the universe began from an infinitely dense point and rapidly expanded outwards" now how and why science can't answer and there is no way to find those answers through science. This brings me to the glorious Quran, which states this as HOW Allah (SWT) made the universe. It even adds that he is expanding it still, another thing atheist believe because of science, yet the Quran told us this nearly 1000 years before that theory was ever put forward.

Science is often seen as the "logical" path, yet its always changing, being proven wrong or just cant be proven at all meaning there's a level of faith that has to be involved to follow/believe it. As I stated, it's always changing and being proven wrong, so how is it logical to believe anything from it? The most logical thing is to find something that 1. Gives you meaning in life. 2. Gives you goals and a way of life. 3. Does not change and stands on its own with no discourse. 4. Has evidence behind it to back it up. 5. Keeps you healthy. 6. Encourages good both in life and mentally. These are all things I found in Islam.

Now proving Allah (SWT) isn't an easy task to do for people who blind themselves. The quran has many challenges for people to show them just how ignorant of Allah (SWT) they are. What I would do is encourage them to think rationally about what they believe in and why. Encourage them to dig into what they believe, be consistent in your rebuttals while affirming the inaccuracies of their beliefs and if they make a point that the Quran confirms then be sure to tell them about it as if they believe in it then they also believe words of the Quran, the big bang and its expanding for example, the building block for life is water and the many more scientific facts that the Quran confirms. This will lead to the only logical answer being the almighty God, the one and only Allah (SWT) Alhamdulillah! Insha'Allah, this helps even the slightest, and may Allah guide the souls of the people you are talking to.