When can I recover the input tax I incurred before tax registration?

If you purchased taxable supplies before registering for VAT, you can recover the taxes levied for those supplies in the first tax period following your tax registration. 

For example, let us consider a simple case involving a retailer. Mr. Saahil owns a leather products shop in the UAE. He imported some leather goods in January 2018, then registered for VAT in March 2018, so he can recover his input tax on his first tax period.