CAN WE SEND GOODS WITHOUT E-INVOICE

You can send the material on approval basis and prepare the invoice after work completion. your customer suggestion is proper and accordance with rules.

Yes but how to send material to the site?

Through e-way bill which having multiple option kindly refer e-way bill guidelines.

On Delivery Challan & as per FAQ available on CBIC site E-invoice is not applicable on DC.

Generally the in case of contractor services it's is cover U/s 2(33) "Continues Supply of Services " & in case of Continues Supply of Services The Invoice is raise as per the provisions of Section 31(5) :
1. Where the due date of payment is ascertainable from the contract : Tax Invoice & E-invoice need to be Issue on or before due date of payment.
2. Where the due date of payment is not ascertainable from contract: Tax Invoice & E-invoice need to be issued on payment received.

3. Where the Payment is linked to the Completion of an event: Tax Invoice & E-invoice need to be on Completion of Event.

Note : Moreover it is issued on Completion of Event. So in between during the goods can be supplied on DC as per provisions prescribes in Rule 55.