Once you have paid the user fee, the issuance of the Estate Tax Closing Letter (ETCL) depends on the presence of the TC 421 transaction code on the account transcript. The TC 421 signifies that the return was accepted as filed or that any examination of the return has concluded.
If the TC 421 is already present on the transcript and the payment is verified, the ETCL will be issued. However, if you make the request and pay the user fee before the TC 421 is present on the transcript, the request will be held and monitored every 30 days until the TC 421 posts. Once the TC 421 posts, the ETCL will then be issued.
Therefore, the timing of receiving the ETCL is contingent upon the TC 421 being posted on the account transcript and the verification of the payment.
Sources:
IRS FAQ