"Groundhog Day" was always planned for Broadway first.
To quote Michael Riedel columns may be specious, but those were the ones I found first, and his headlines tell the whole story:
On April 2, 2015, his headline announced "Scott Rudin is bringing Groundhog Day to Broadway"...
On June 21, 2016, when Scott Rudin dropped out after a NY workshop (supposedly because he wasn't having the kind of control he prefers),
Riedel's headline read "Groundhog Day musical is in Big Trouble".
Presumably, had the first production at the Old Vic not gone well, it wouldn't have transferred to either a Broadway OR West End venue.
Then performances began.
On August 18, 2016, Riedel wrote "Broadway producers are terrified of Groundhog Day" - with rivals speculating/fearing whether it would come in this year or not, saying "the raves caught much of Broadway off guard".
On September 13, 2016, his headline was "Groundhog Day" is coming to Broadway this season". (Even though, he adds, "Sources on “Groundhog Day” say the creators are not so arrogant as to think they have a perfect show. “They will be doing a lot of work between now and the spring,” a source says.)
So, long story short, it came to Broadway because they always wanted it to,
and because the rave reviews from both U.S. and UK press, and the box office and audience response, all agreed it deserved to