It depends on what ones opinion is on what is a Big Time Player... IMO, one cannot forecast when a lady will or could become a household name or Big Time Player.
Some may think its playing at a power 5 school, others any level of post secondary play, national team play, getting paid to play etc.
There are ladies that never played any high level travel that made it to the college game at all levels, others that played at a smaller school or community college that went on to a power 5 school, the professional ranks or found their way on a national team.
I have seen ladies in their younger years that were ahead of their peers 8 through 13 years old and dominated then, peeked at 14ish.
Also some that was behind their peers that bloomed after 14 or 16. By 18 there are the ladies may have the talent but not the desire to continue.
Opportunities also present themselves in different ways as connections can elevate ones standings or that diamond in the rough gets found. There are a lot of stories where players talk about their journeys. Some the traditional travel at a high level that resulted in opportunities for them others where it did not appear they would play past HS then things turned in their favor.