In order for you to build some trust in them, the first step, I'd think, is for you to read their
Privacy Policy and learn about what data they collect when you use their services and what they do with it.
A common myth is that Google sells your personal data to advertisers, but they do no such thing, nor is someone at Google personally looking at your data. Rather, a computer does it and this is used to both improve their services, something which you end up benefiting from, and also to show you more relevant advertisements, which is how Google turns a profit and what allows them to offer so many great services for free.
Yes, indeed, Google does ends knowing a lot about yourself if you decide to jump into their ecosystem and user their services to their full (in truth, so do Apple and Microsoft). But is that really a problem? Personally I don't think so.
If you are concerned about your data being safe with them, know that it is in their best interests to safeguard it given that the value and usability of their products and services is entirely dependent on them actually having, organizing and making useful said data.
In the end, any company with an ecosystem of integrated hardware, software and services like Apple, Google and Microsoft have will want to obtain your data to better improve their products, it is just how it works. The question is basically about trust and what ecosystem you like better. Not whether any of these companies are actually gathering your data or not.