USCIS has produced a simple chart explaining when E-Verify and I-9s can and must be completed for new hires.
Completing Form I-9 and E-Verify
The earliest you may complete Form I-9: The employee has accepted
an offer of employment
The earliest you may create a case in E-Verify: The employee has accepted
an offer of employment and Form I-9 is complete
The latest you may complete Form I-9: The third business day after
the employee started work for pay
The latest you may complete E-Verify: The third business day after
the employee started work for pay and Form I-9 is complete