I have tried datepart(wk, Date). It groups by week (datepart(wk, Date)) and then displays the first entry of that week, not the first day in the week, necessarily

select DOP_ID,

(First_Name + ' ' + Last_Name) as Name,

Category,

min(Date) as WeekOf,

sum(Hours) as TotalHours

FROM [GW_PPP].[dbo].[SLAM_Attendence]

where DOP_ID in (select DOP_ID from [GW_PPP].[dbo].[SLAM_Status] where STATUS ='Enrolled')

and Category in ('GED Program', 'Lit/Num Combined (Pre-GED)')

group by DOP_ID,Category, datepart(wk, Date)