Is there a quick way to get to the phone's keypad after answering the phone

More and more now, there are automated machines that want to call us back, and they want us to enter information via touch tone. I encountered this with Uber recently, when attempting to report an item that was left in the Uber car. Uber's automated machine had to call me back to take more info. However, I didn't have enough time to get to the phone's keypad to enter info in. Then recently, a friend of mine told me of an incident where Apple was calling him back because he was reporting an issue he had with his account, however, again, he was asked to enter in information, but could not get to the keypad quick enough. That is the downside of answering the phone and the phone not being in focus straight away.
Has anyone any solution to the problem? I'm using an iPhone SE2 with the latest iOS update, btw.
And I do have multiple ways to use the keypad, such as using my bt keyboard, or my Orbit reader 20. But, needing to get there quickly after answering the phone, that is another story.