You can’t ask curl to try all available protocols for a single request, but you can force it to use a specific version of HTTP:
curl --http1.1 "https://www.aeromexico.com/en-us/am-news/new-Rome-route" -s --trace-ascii -
The available variants are --http0.9, --http1.0 (or -0), --http1.1, --http2, and --http3.