How to Use "～し始める"
し始める = To start doing something.
読み始めた, 泳ぎ始めた, 歩き始めた...etc
私は、４歳の時から新聞を読み始めた
=I started reading a paper when I was four years old.
Do not say "～して始める".
It means "to do and start doing something".
If you said "私は、４歳の時から新聞を読んで始めた".
That sounds like you read a paper and then started doing something when you were four years old.
