Now that I am older, I believe .... (Para. 7)
Meaning: Because I am older, I believe... .
Here "now that" is used as a conjunction, meaning "since" when we are talking about the effect of an event or change. This conjunction can be shortened to "now". For example:
Now (that) John has arrived, we can begin. 既然约翰来了, 我们可以开始了。
Now (that) she's found him, she'll never let him go. 既然她找到了他, 就决不会放他走了。
I like him a lot now (that) he's older. 他现在老了, 我倒十分喜欢他。