Get the First activity based on date column

Sri_phani Try this. PBIX is attached below signature.

Measure = 
    VAR __Emp = MAX('Table'[Employee Name as per IROZ])
    VAR __Table = FILTER( 'Table', [Extracted Activity Name] = "Break_Unpaid" )
    VAR __MaxBreakStart = MAXX( __Table, [Activity start IST/EET] )
    VAR __MaxBreakEnd = MAXX( FILTER( 'Table', [Activity start IST/EET] = __MaxBreakStart ), [Activity end IST/EET] )
    VAR __BreakStartTime = __MaxBreakStart - TRUNC( __MaxBreakStart )
    VAR __BreakEndTime = __MaxBreakEnd - TRUNC( __MaxBreakEnd )
    VAR __Result = FORMAT(__BreakStartTime, "Medium time" ) & " - " & FORMAT( __MaxBreakEnd, "Medium time" )
RETURN
    __Result

hi Sri_phani ,

as per the data available in the mentioned link the minimum time for break on 26th Jul should be 12.45 PM.

After considering this, if I proceed then I have done the following steps

Filter the table with respect to Break_Unpaid

Calculating first break

Please check visualization

Now if you need the yellow/red highlighted time as first break then either max function or distinctcount function (if there are more than 2 break periods available for an employee per day) needs to be used.
Using max function

Using Distinctcount function

Visualization can be done in the similar way.

If this solves your problem then accept the same as your solution.