They said they have considered it and decided against it. Likely for good reasons.

Using AWS as a "temporary solution" is a suggestion born from ignorance - it is not a solution to the temporary problem we have now.

AWS doesn't magically just scale without effort. You need expertise to specifically design for it, otherwise you risk making things worse.

You can't simply copy-pasta your way into AWS. We're talking about complex infrastructure that was not built for cloud in the first place.
They would be looking at a migration process that takes months to years of planning, executing and testing.

Even if we entertain the fantasy that they could "just AWS 4head" in 2 days - migrating to a completely different environment for a temporary problem is a completely stupid business decision.

TLDR: AWS is not magic, stop pretending it is.