AWS Cognito sending SMS?

Question

Amazon Web Services

Is it possible to change the provider for delivering SMS when verifying the phone?
For example, for MFA, using 3 lambdas ( Define Auth Challenge , Create Auth Challenge and Verify Auth Challenge Response ) I can custom send a message with a code through another provider, and then check if the code matches. But for phone / email confirmation, I did not find anything like that.
There is a Custom message lambda trigger, but you can only change the message template in it. I can custom send the code, but I don’t understand how Cognito can tell what code I sent and with what to compare.
Or is there an easier way to change SNS to Twilio?