"No line to add 1099-G in Schedule C why not put it on 1040 Schedule 1 line 8z under other income so this way client does not have to pay Selective Employment tax."

I think you mean Self-Employment Tax. Yes, it is subject to SE Tax. It is Business Revenue. It is not "other." That's the wrong way to do this.

1099-G box 6 issued to a business for a grant that does not fall under one of the exemptions is treated as ordinary business income and included the same as any business gross income, without also needing to enter the 1099-G. There are a lot of these grants relative to the covid disaster and the various recovery and stimulus programs, so ask your client to help you identify what their application was for and what grant they were given, to know how to treat it for Fed and State purposes.