E Way bill -Export

As per Rule 138 of CGST Act , Eway is required to be generated only when there is movement of Goods subject to conditions prescribed therein.
As per Section 31 ,R/w Rule 48(4) of CGST Act a registered person supplying goods shall Before or At the time of removal of goods shall issue the Tax Invoice.
In above kindly note the word "before" which is not define, so can be any time but for the movement of goods the Eway Shall generated at that time because the validity period has been define rule 138(10).

As under rule 48(4) notified person whose aggregate turnover is 50crore in Preceding FY ,from 1/4/2021 the E-invoice is applicable and as in your case the movement of goods is in month of April 2021 so you are required to generate E-invoice & Eway bill for the Invoice being issued on 31/3/2021.The law does not specifically provide any time limit for E-invoice to be generated , but before the transportation of goods the E-invoice need to be generated. So there shall be no problem in that the Tax Invoice is raised on 31//3/21 & E-invoice & Eway is generated at time of transportation of Goods

Note :

As EVEN THOUGH THE E-invoice is valid document But .....THE PROBLEM can be ARISE WHEN SUCH GOODS ARE BEING INTERCEPTED BY PROPER OFFICER DURING THE TRANSIT, THE OFFICER CAN OBJECT ON THE DATE OF TAX INVOICE & CAN ISSUE ORDER FOR DETENTION U/S 129.

SO TO AVOID SUCH LITIGATION THE INVOCIE SHOULD BE RAISED ONLY WHEN THE GOODS ARE READY TO DELIVER.