The current implementation use a ping to check the connectivity. It's better to make a check on http port as it is what we need next to use the time API.
OTA script can be a source of inspiration for that if the execution speed is correct.
It would be great to find a target website accessible from everywhere (may be worldtimeapi.org ).

It worth to check where we use ping commands at the same time as ICMP can be blocked on some user internet connections.