Honestly, I doubt it can truly be the cases however it could make sense with the overall context for this ability.

I ultimately came to this idea that "Star Platinum" technically, always had the time stop ability however Jotaro didn't realize this until his fight of Dio. Now I did use a external source that I use a few of points off for this conclusion but not entirely because I don't think it would just make sense that "Will power and believing" alone can let a stand stop time but who knows about that. I am focusing on why I believe the "Star Platinum always had it" notion.

When it comes to the story: Star Platinum is considered a fast short range stand, similar to Dio's stand "Za Warldo". Before the fight or the realization of Za Warldo stopping time, Jotaro may have interpret SP "fast speeds" as just fast speeds because there was a lack of indication to him and the others of the idea that SP could do this ability as they didn't know a stand could stop time.

Infact, you can interpret the moments like in the beginning of the part (When Jotaro was in prison and he had a gun against his head) and the gamble fight of Jotaro against D'arby (SP lighting Joraro's cigarette and giving him a drink) as moments when Star Platinum did stop time but like I said early "they didn't know a stand could stop time" so moments like this would seen as SP being fast.

Jotaro knowing that the "Za Warldo" can stop time, the fact SP is similar to that stand and maybe some other reasons did gave Jotaro a reference point and the eventual conclusion that "Star Platinum can stop time" and finally was able to use it properly against Dio after being crushed by the road roller.

In summary, SP did had the time stop ability but Jotaro never realize it until his fight with Dio.

I'm not making him look stupid about this possibility btw