Non-compete

My company “A” currently sub-contracts for consulting company “B” who sub-contracts with company “C” onsite at company “D”.

My company “A” does NOT have a non-compete with “B” and has no contract with “C”. Consulting company “B” Does have a non-compete with “C”.

Can my company go do work for “D” directly since my company “A” has no non-compete?