Clarification needed

I was practicing typing in Japanese with a classmate of mine and wanted to type: (…) time began moving too fast.

I thought of two ways of saying it, but I don't know which is more correct/natural or if they both are correct but convey slightly different meanings.

So:
1) 時計の針は、速くなりすぎた。
2) 時計の針は、速すぎになった。

I'm sure there are "better"/more natural ways to say this, but I'm still at an N4ish level.

Thanks in advance to any respondents 🙏