QBI for non-1099 work?

[gotstogo]

I am working as an engineer in a side gig.  I recently started doing work for a previous company (two jobs ago and 6+ years ago), and I am being paid through a contract agency.  I didn't realize that I was being paid as an employee of the contract agency vs. as a 1099 until after accepting the work and invoicing a few times.  I am working from home, not in the business location.  I am also supplying all the equipment needed for the job (computer, software, technical books, internet, etc.).  And, I do not receive any benefits from the contract agency.   They are withholding small amounts of taxes, SocSec, SDI and Medicare.  Can I still claim this income as QBI even without a 1099 and likely a W2?

[Anonymous]

if they're withholding payroll taxes you should get a w-2 as an employee. Employee is not a business for purposes of the QBI. 

[Critter]

And an employee cannot deduct any business expenses.  When you started working for this agency they must have had you fill in a W-4 form and the "paycheck" would have shown the FICA withholding so being treated as an employee should not have been a surprise.