Extract a list of numbers under multiple criteria to another workbook

Hello all,

I have been trying for days to extract a list of numbers (Emp. ID) which will be under multiple criteria.
For example;

1st sheet has the expected employee data (Designation, Site, Pay etc)
2nd sheet has actual Emp Id, designation and Site

What I need is to get the Emp ID of the actual employee under site/designation in sheet 2 to sheet 1 matching the site/designation in sheet 1.

I was successful using following

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which returned the EmpID for me. (AND contains the matching I did with the two sheets and vlookup has the EmpID and other stuff needed)

But I got hit with error where the Site is not sorted but has several sites in the list. Sheet 1 is sorted by Emp ID which is not the same for sites.
I dont need to run macro on this but can anyone help me on this please.

Anyone knows how to use vlookup with multiple criteria or find the next matching text (site) in a list to give the corresponding row number which would continue looking down the list for the text...

Thanks in advance...