No, it is not too late! Only the first round of Economic Impact Payments have been distributed as of today (April 15, 2020.) A large number of taxpayers are still on the list to get payments and the IRS has not given us any indication that lets us know whose payments are being sent in what order.
Since you just filed a few days ago, I would expect that you would receive your payment sometime after your return is processed though exactly how long that may take is not known.
The nonfilers application is actually just a simple 1040 tax return, so it would not have been any quicker than filing your actual return the way that you chose.
By doing it the way that you did, you actually saved yourself some additional work down the road!
Any taxpayer whose advance payment received is less than the full payment for which he or she is entitled, will be eligible to claim the difference as a credit on the 2020 tax return filed in 2021. That is the latest date at which you would receive the payment.
Please check these links frequently for updates:
Economic Impact Payments
TurboTax Updates
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