I think there are maybe two simultaneous routes.
Firstly, the Catholic church itself.
If there is such a thing as Truth, then we ought to recognise it. It has a power that we should feel when we come across it.
When I read the writings of the Church they have the ring of truth. I find them stirring some inchoate sense of truthfulness that leaps inwardly at the sound of it.
Perhaps you have read pieces of wonderful writing that evoke a similar response in you. A sort of gratitude that the writer has articulated something that you feel to be 'true'.
There is some reading here but it is very heavy.
And the Catechism is here.
I don't think it is necessary to be a catholic, or even a believer of any sort, to appreciate the weight of the words, which, at the very least demand our attention. There really is little point reading it in a cynical frame of mind though.

The other route, which could be undertaken simultaneously, is to discern whether the God of the bible is true. And therefore also, whether the Jesus of the bible was who he claimed to be. That's a big one, and obviously a huge stumbling block for someone who is an avowed atheist.
I will say that there are innumerable very sane and level headed atheists and agnostics who came to believe through being persuaded by the biblical account of the resurrection.
Once that falls into place, you can accept the idea of a God who entered space and time and remains with us in some way.
All Christians accept the concept of a church, but they have different concepts of what that means. Some Christians see the church as being a purely spiritual thing. An invisible body of believers, rather than an actual institution.
Catholics see it as both.
The catholic concept of church however, is much more congruent with the scriptural accounts and also with the historical church, about which we know a great deal.
I'm wrapping up quickly here because it's so late and I need to get off the computer .
There is a great deal to say about this and I can't put it all in one comment.
More anon, but feel free to add any other objections etc.