It is impossible to estimate when the IRS will cash the check. Mailed returns are sitting in stacks unopened until the IRS works through the backlog and finally opens them. They have indicated they will be processed based on when they were received so a return mailed now will likely be at the bottom of the pile.
If you want to know exactly when the payment will be made, use IRS direct pay to make the payment instead of mailing a check with your return and waiting for the check to be cashed: https://www.irs.gov/payments/direct-pay
